1) The sample proportion is 0.14 (7 left-handed students out of 50 total students surveyed).
2) The hypothesized proportion po is 0.10 (the usual proportion of left-handed students).
3) The sample size n is 50 (the number of students surveyed).
4) The test statistic z is 1.32.
1) The sample proportion is calculated by dividing the number of left-handed students by the total number of students surveyed. In this case, 7 left-handed students out of 50 gives a sample proportion of 7/50 = 0.14.
2) The hypothesized proportion (p₀) is the usual proportion of left-handed students, which is given as 0.10.
3) The sample size (n) is the total number of students surveyed, which is 50.
4) The test statistic (z) can be calculated using the formula: z = (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size). In this case, z = (0.14 - 0.10) / sqrt((0.10 * (1 - 0.10)) / 50) = 0.04 / sqrt(0.09 / 50) ≈ 0.943.
To calculate the test statistic z, we use the formula:
z = (sample proportion - hypothesized proportion) / standard error
The standard error is calculated as:
standard error = sqrt((po * (1-po)) / n)
Plugging in the values, we get:
standard error = sqrt((0.10 * (1-0.10)) / 50) = 0.0499
Then,
z = (0.14 - 0.10) / 0.0499 = 1.32
Since the calculated z-value of 1.32 is greater than the critical value of 1.645 (using a significance level of 0.05 for a two-tailed test), we can conclude that there is not enough evidence to reject the null hypothesis that the proportion of left-handed students at the school is the same as the usual proportion of 0.10.
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A, B, C and D lie on the circle, centre O.
TA is a tangent to the circle at A.
Angle ABC = 131° and angle ADB = 20°.
Please Find
Angle ADC =
Angle AOC =
Angle BAT=
The value of angle ADC is 131⁰.
The value of angle AOC is 262⁰.
The value of angle BAT is 21⁰.
What is the value of angle ADC?The value of angle ADC is calculated as follows;
The value of the angle at center, AOC = 2 ∠CBA (angle at center is twice angle at circumference)
∠AOC = 2 x 131⁰
∠AOC = 262⁰
The value of arc angle ABC = 262⁰ (intersecting chord theorem)
The value of angle ADC is calculated as;
∠ADC = ¹/₂ arc ABC
∠ADC = ¹/₂ x 262⁰
∠ADC = 131⁰
Angle DAB = 180 - (20 + (131 - 20))
∠DAB = 180 - 131 = 49
The value of angle BAT is calculated as;
∠BAT = 90 - (20 + 49)
∠BAT = 21⁰
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Write the function in terms of unit step functions. Find the Laplace transform of the given function.f(t) =0, 0 ≤ t < 1t2, t ≥ 1
The Laplace transform of the given function f(t) is [tex]L{f(t)} = (2/s^3) ~e^{-s}[/tex]
We have,
The given function can be represented in terms of unit step functions as follows:
f(t) = 0 for 0 ≤ t < 1
f(t) = t² for t ≥ 1
Using the unit step function u(t), we can express f(t) as:
f(t) = 0 x u(t) + t² x u(t - 1)
Apply the linearity property of the Laplace transforms and use the Laplace transform of the unit step function u(t-a), which is [tex]1/s ~e^{-as}:[/tex]
[tex]L{f(t)} = L{0 \times u(t)} + L{t^2 ~ u(t - 1)}\\= 0 \times L{u(t)} + L{t^2} ~ L{u(t - 1)}\\= 0 + L{t^2} ~ e^{-s \times 1}\\= L{t^2} ~ e^{-s}[/tex]
Using the Laplace transform property [tex]L{t^n} = n!/s^{n+1},[/tex] where n is a positive integer,
[tex]L{t^2} = 2!/s^{2+1}\\= 2!/s^3\\= 2/s^3[/tex]
Therefore,
The Laplace transform of the given function f(t) is [tex]L{f(t)} = (2/s^3) ~e^{-s}[/tex]
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Let p be the population proportion for the following condition. Find the point estimates for p and q. A study of 4374 adults from country A, 2903 think mainstream media is more interested in making money than in telling the truth.
The point estimates for p and q are 0.6636 and 0.3364 respectively, where p is the population proportion for the condition.
To find the point estimates for p and q, you will need to consider the given information about the population proportion, follow the given steps:
1. The total number of adults in the study is 4374.
2. Out of these, 2903 adults think mainstream media is more interested in making money than in telling the truth.
3. To find the point estimate for p (the proportion of adults who think mainstream media is more interested in making money), divide the number of adults who think this way by the total number of adults in the study:
p = 2903/4374 = 0.6636 (rounded to four decimal places)
4. Now, to find the point estimate for q (the proportion of adults who do not think mainstream media is more interested in making money), subtract p from 1:
q = 1 - p = 1 - 0.6636 = 0.3364 (rounded to four decimal places)
So, the point estimates for p and q are 0.6636 and 0.3364, respectively.
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How would you write the equation for the graph f(x)=x^2 after it has been shifted to the left 7 and down 4
Step-by-step explanation:
Shift to the L 7 units ( x+7)^2
Shift down 4 (x+7)^2 - 4
Which of the following represent direct variation?
Answer:
all yes
Step-by-step explanation:
Pete's yard is 52.7 feet wide. The length is 30.4 feet greater than the width.
What is the perimeter of Pete's yard in feet?
Answer:166.2 feet^2
Step-by-step explanation:
By assuming that Pete's yard is a rectangle, we can get the perimeter by using an equation that looks like this:
perimeter = l+l+w+w
Where l = length, and w = width.
This is because you are adding the measures of every side together, which is the definition of the value of a perimeter.
Furthermore, to get the area of the figure, you would need to multiply 52.7 by 30.4, which would be 1602.08 feet^2
A new cholesterol medication has been manufactured and a study is being
conducted to determine whether its effectiveness depends on dose. When 25
milligrams of the medication was administered to a simple random sample (SRS) of
50 patients, 17 of them demonstrated a lower cholesterol level. When 65 milligrams
of the medication was administered to another SRS of 40 patients, 10 of them
demonstrated a lower cholesterol level. Which of the following test statistics is an
appropriate hypothesis test?
The statistics that is the most appropriate is option 2 from the image I added. [tex]Z = \frac{0.34 - 0.25}{\sqrt{\frac{0.3(1 - 0.3)}{50}+\frac{0.3(1 - 0.3)}{40} } }[/tex]
How to find the appropriate statisticsWe have to find the proportion 1
= 17 / 50
= 0.34
Then we find the proportion 2
= 10 / 40
= 0.25
the proprotion = 17 + 10 / 50 + 40
= 27 / 90
= 0.3
Then the value of n1 = 50 and the value of n2 = 40
If we are to find the test statistics
The formula that we would use after inputting the values would be given as
[tex]Z = \frac{P1 - P2}{\sqrt{p(1 - p)\frac{1}{n1}+\frac{1}{n2} } }[/tex]
We will have
[tex]Z = \frac{0.34 - 0.25}{\sqrt{0.3(1 - 0.3)\frac{1}{50}+\frac{1}{40} } }[/tex]
When we expand we will have
[tex]Z = \frac{0.34 - 0.25}{\sqrt{\frac{0.3(1 - 0.3)}{50}+\frac{0.3(1 - 0.3)}{40} } }[/tex]
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Please guys I need help bad it's dew tomorrow
Answer: The answer is A (40 m)
Step-by-step explanation:
The frequency of people compared to the number of monthly text messages sent and received by a class are shown in the histogram.
Answer: The data is skewed because most text messages are replied to and cause the number to be at least twice what it was originally.
Step-by-step explanation: The data is left-skewed.
Bethany uses the equation d=3. 75h to find the distance, d, she travels while walking for h number of hours. What is the constant of proportionality between d and h? show your work
The constant of proportionality between d and h is 3.75
Any function in which the dependent variable (y) is obtained by multiplying the independent variable (x) by a constant value is called the direct proportionality function. This function is also expressed in the form [tex]( y = m * x)[/tex] and is more commonly called a linear function.
The value m is a constant and is known as the constant of proportionality or the slope of the line. It represents the inclination of the line to the abscissa axis, that is, the x-axis. If we talk about graphic representation, this linear function is a line with slope m that passes through the origin of coordinates, that is, the point 0 in x and 0 in y, which is the point (0,0).
Bethany finds the distance d with the help of equation d = 3.75*h, she travels this distance while walking for h number of hours. When we compare it with the direct proportionality function y = m * x, then y is represented by the distance d, x is represented by the number of hours h, and slope m or the constant of proportionality is the number 3.75.
So, the constant of proportionality between d and h is 3.75.
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Answer two questions about Equations A and B: A. 5x = 3x B. 5 = 3 1 ) How can we get Equation B from Equation A?
We cannot get Equation B from Equation A as they are fundamentally different.
Equation A, 5x = 3x, is a linear equation with variables on one side and constants on the other side. To solve this equation for x, we can subtract 3x from both sides to get:
5x - 3x = 2x
Therefore, the solution to Equation A is x = 0 or x = any other real number.
On the other hand, Equation B, 5 = 3, is a statement of equality between two constants. There is no variable in this equation to solve for, and it is always false since 5 is not equal to 3.
Thus, there is no way to derive Equation B from Equation A or vice versa.
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Complete the following using present value. (Use the Table provided. ) (Do not round intermediate calculations. The "Rate used to the nearest tenth percent. Round the "PV factor" to 4 decimal places and final answer to the nearest cent. ) On PV Table 12. 3 Rate used PV factor used PV of amount desired at end of period Period used Length of time Rate Compounded Amount desired at end of period $ 9,800 % 4 years 6% Monthly
The present value of $9,800 at the end of 4 years with a 6% monthly compounded rate is $7,996.84.
To find the present value of $9,800 at the end of 4 years with a 6% monthly compounded rate, we need to use the present value table.
First, we need to find the monthly compounded rate. The annual interest rate is 6%, so the monthly rate is
6/12 = 0.5%
Next, we need to find the PV factor. From the present value table 12.3, the PV factor for 48 periods at 0.5% monthly rate is 0.8138.
Now, we can calculate the present value:
PV = 9,800 × 0.8138
=7,996.84
Therefore, the present value of $9,800 at the end of 4 years with a 6% monthly compounded rate is $7,996.84.
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Assume that blood pressure readings are normally distributed with a mean of 125 and a standard deviation 4 probability that their mean blood pressure will be less than 127. a) 0.0070 b) 0.6681 c) 0.8245 d) 0.9930
This value is the same as the value found in the z-table: P(X < 127) = 0.6915 The closest answer to this value is option (b) 0.6681.
We'll use the z-score formula and a standard normal table (z-table) to find the probability.
The given terms are: - Mean (μ) = 125 - Standard deviation (σ) = 4 - Target blood pressure (X) = 127
Step 1: Calculate the z-score using the formula: z = (X - μ) / σ z = (127 - 125) / 4 z = 2 / 4 z = 0.5
Step 2: Use a z-table to find the probability that corresponds to the z-score. In this case, the z-score is 0.5. The value found in the z-table for a z-score of 0.5 is approximately 0.6915.
Step 3: The probability that the mean blood pressure will be less than 127 is the area to the left of the z-score (0.5) in the standard normal distribution.
This value is the same as the value found in the z-table: P(X < 127) = 0.6915 The closest answer to this value is option (b) 0.6681.
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6. Gomer has a super-jumbo-sized drip coffee maker. The beverage is produced as hot water filters
through a cone-shaped vessel containing coffee grounds. The cone has a height of 3 inches and diameter
of one foot. Assuming that the cone is filled with water, and the water is dripping out at a rate of 10 cu.
in. per minute, how long will it take for all of the water to pass through? HELPPP
It will take time of 33.93 minutes for all of the water to pass through the cone.
To find the volume of the cone-shaped vessel, we need to use the formula for the volume of a cone:
V = (1/3) x pi x r² x h
V = (1/3) x 3.14 x 6^2 x 3
= 339.29 cubic inches
This is the total volume of water that needs to pass through the cone.
If water is dripping out at a rate of 10 cubic inches per minute, we can use the formula:
time = volume / rate
to find how long it will take for all of the water to pass through. Substituting the values we found, we get:
time = 339.29 / 10
=33.93 minutes
Therefore, it will take 33.93 minutes for all of the water to pass through the cone.
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How to apply the inverse of sine so that you can give your final answer of the measure of X in degrees?
In a right-angle triangle, a sine function of an angle [tex]\theta[/tex] is equal to the opposite side to [tex]\theta[/tex] divided by hypotenuse.
[tex]\text{Sin} \ \theta = \dfrac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
How do you find the inverse of a trig function?[tex]\text{y = f(x)} \rightarrow \text{x}[/tex] in the domain of f. Trigonometric functions are periodic, therefore each range value is within the limitless domain values (no breaks in between). Since trigonometric functions have no restrictions, there is no inverse.
The inverse sine function (also called arcsine) is the inverse of sine function. Since sine of an angle (sine function) is equal to ratio of opposite side and hypotenuse, thus sine inverse of same ratio will give the measure of the angle. Let’s say [tex]\theta[/tex] is the angle, then:
[tex]\text{Sin} \ \theta = \dfrac{\text{Opposite side to} \ \theta}{\text{Hypotenuse}}[/tex]
[tex]\text{Or} \ \theta = \text{Sin-}1 \ \dfrac{\text{Opposite side to}\ \theta}{\text{Hypotenuse}}[/tex]
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student has a bucket that consists of the first 20 positive integers. count the number of ways the student can pull 5 integers out of the bucket in increasing order. for example, the student could take out 3, 6, 10, 11, and 18 in that order. however, if they take out 4, 3, 6, 18, and 1, then we do not count this (because it is not increasing).
The number of ways the student can pull 5 integers out of the bucket in increasing order is 15,504.
To determine this, we can use the combination formula, which calculates the number of ways to choose k objects from a set of n objects, regardless of order. In this case, we want to choose 5 integers out of a set of 20 integers in increasing order, which means we can use the combination formula with repetition: C(n+k-1, k-1).
Substituting in our values, we get: C(20+5-1, 5-1) = C(24, 4) = (24232221)/(4321) = 15,504.
Therefore, there are 15,504 ways for the student to pull 5 integers out of the bucket in increasing order.
It is important to note that the order of the integers matters when counting the number of ways in which they can be chosen. In this case, the integers must be chosen in increasing order, which means we cannot count combinations where the integers are chosen in a different order. For example, choosing 1, 2, 3, 4, and 5 is a valid combination, but choosing 5, 4, 3, 2, and 1 is not, since the integers are not in increasing order.
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what time what equals -20 but also adds to -8
Answer:160
Step-by-step explanation:
multiply the expressions
which pair of points should be used to find the line of best fit for the scatter plot?
*picture*
J and L
J and M
K and L
K and M
The pair of points to be used is k and M.
What is line of best fit?A line of best fit is a straight line which is used to show the relations among non-linear points in a scatter plot. Thus it evenly varies the points on its two sides. This is majorly used when dealing with a cartesian coordinate, or plotted points on a graph.
Considering the given scatter plot, it can be observed that points J, L, M and K on non-linear. Thus the straight line that can be used to as line of best fit is by joining point K and M.
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Vanessa bought 2.67 pounds of pasta salad at the deli. Charlie bought 1.65 pounds of pasta salad. how much more pasta salad Vanessa buy than Charlie?
Answer: 1.02
Step-by-step explanation:
2.67 - 1.65 = 1.02
In order to solve a system by substitution, you want to...
*
get opposite coefficients for each variable in each equation.
get opposite coefficients for one set of variables in each equation.
isolate a variable in an equation and then substitute into the other equation.
put the corresponding augmented matrix into RREF (row reduced echelon form).
In order to solve a system by substitution, you want to isolate a variable in one equation and then substitute it into the other equation.
Given that;
To complete the sentence for solving the system of equation.
Now, We know that;
Once you have substituted the variable, you can solve for the remaining variable(s) and find the solution to the system.
Hence, In order to solve a system by substitution, you want to isolate a variable in one equation and then substitute it into the other equation.
Therefore, Option C is true.
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roland received a score of 70 on a test for which the mean score was 65.5. Roland has learned that Z-score for his test 0.6. What is the standard deviation for this set of test scores?
If Roland has Z-score for his test 0.6, the standard deviation for this set of test scores is 7.5
To find the standard deviation for this set of test scores, we can use the z-score formula:
Z-score = (X - μ) / σ
Where:
- Z-score is 0.6 (given)
- X is Roland's score of 70
- μ is the mean score of 65.5
- σ is the standard deviation we need to find
Now we can plug in the values and solve for σ:
0.6 = (70 - 65.5) / σ
Next, we can rearrange the equation to solve for σ:
σ = (70 - 65.5) / 0.6
Finally, calculate the standard deviation:
σ = 4.5 / 0.6
σ ≈ 7.5
The standard deviation for this set of test scores is approximately 7.5.
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What degree of measurement is
5
8
of a circle?
Answer: 225 degree
5/8of full rotation is 225degrees
Answer:
0.625
Step-by-step explanation:
hope the his helping
2. Jade is 6 years less than twice Kevin's age. 2 years ago, Jade was three times as old as kevin. How old was Jade 2 years ago? 3. Len is 2 less than 3 times Amanda's age. 3 years from now, Len will be 7 more than twice Amanda's age. How old will Amanda be 3 years from now? 4. Janna is twice as old as Faith and William is 9 years older than Faith. 3 years ago, janna was 9 less than 3 times Faith's age. How old is William now?
William is currently 15 years old.
Let's start by using algebra to solve for the ages of Jade and Kevin now. Let J be Jade's current age and K be Kevin's current age. We have:
J = 2K - 6 (Jade is 6 years less than twice Kevin's age)
J - 2 = 3(K - 2) (two years ago, Jade was three times as old as Kevin)
We can use the first equation to substitute for J in the second equation:
(2K - 6) - 2 = 3(K - 2)
Simplifying this, we get:
2K - 8 = 3K - 6
K = 2
So Kevin is currently 2 years old, and Jade is:
J = 2K - 6 = 2(2) - 6 = -2
This doesn't make sense as an age, so there may be an error in the problem statement or in our solution method.
Let's use algebra to solve for Amanda's current age, which we can call A. Then we can use that to find her age 3 years from now. We have:
L = 3A - 2 (Len is 2 less than 3 times Amanda's age)
L + 3 = 2(A + 3) + 7 (three years from now, Len will be 7 more than twice Amanda's age)
Substituting the first equation into the second, we get:
(3A - 2) + 3 = 2(A + 3) + 7
Simplifying this, we get:
A = 5
So Amanda is currently 5 years old, and her age 3 years from now will be:
A + 3 = 5 + 3 = 8
Let's use algebra to solve for Faith's current age, which we can call F. Then we can use that to find Janna's and William's ages. We have:
J = 2F (Janna is twice as old as Faith)
W = F + 9 (William is 9 years older than Faith)
J - 3 = 3(F - 3) - 9 (three years ago, Janna was 9 less than 3 times Faith's age)
Substituting the first two equations into the third, we get:
(2F) - 3 = 3(F - 3) - 9
Simplifying this, we get:
F = 6
So Faith is currently 6 years old, Janna is:
J = 2F = 2(6) = 12
and William is:
W = F + 9 = 6 + 9 = 15
Therefore, William is currently 15 years old.
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Suppose the following estimated regression equation was determined to predict salary based on years of experience. Estimated Salary=21,640.90+2456.42(Years of Experience) What is the estimated salary for an employee with 18 years of experience?
The estimated salary for an employee with 18 years of experience is $65,856.46.
To find the estimated salary for an employee with 18 years of experience using the given regression equation, follow these steps:
1. Identify the regression equation: Estimated Salary = 21,640.90 + 2456.42 (Years of Experience)
2. Substitute the given years of experience (18 years) into the equation:
Estimated Salary = 21,640.90 + 2456.42(18)
3. Multiply 2456.42 by 18: 2456.42(18) = 44,215.56
4. Add 21,640.90 to the result from step 3: 21,640.90 + 44,215.56 = 65,856.46
The estimated salary for an employee with 18 years of experience is $65,856.46.
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In Exercises 7-10, show that {u1, u2} or {u1, u2, u3} is an orthogonal basis for R2 or R3, respectively. Then express x as a linear combination of the U?s
To express any vector x as a linear combination of an orthogonal basis {u1, u2} or {u1, u2, u3} for R2 or R3, respectively, we can solve a system of linear equations where each equation corresponds to one component of the vector x.
To show that {u1, u2} is an orthogonal basis for R2, we need to prove that u1 and u2 are orthogonal (perpendicular) to each other and that they span the entire space of R2. In other words, any vector in R2 can be expressed as a linear combination of u1 and u2.
Similarly, to show that {u1, u2, u3} is an orthogonal basis for R3, we need to prove that u1, u2, and u3 are pairwise orthogonal and that they span the entire space of R3. Any vector in R3 can be expressed as a linear combination of u1, u2, and u3.
Once we have shown that {u1, u2} or {u1, u2, u3} is an orthogonal basis for R2 or R3, respectively, we can express any vector x in terms of the basis vectors as follows:
For R2:
x = c1u1 + c2u2, where c1 and c2 are constants.
For R3:
x = c1u1 + c2u2 + c3u3, where c1, c2, and c3 are constants.
We can find the values of c1, c2, and c3 by solving a system of linear equations, where each equation corresponds to one component of the vector x. The solution to the system will give us the coefficients that express x as a linear combination of the U.
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If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is
a. 0.5
b. 1/32
c. zero
d. larger than the probability of tails
Each coin toss is an independent event, meaning that the outcome of the previous toss does not affect the outcome of the next toss. Therefore, the probability of getting heads on the fifth toss is still 0.5.
The scenario you've described involves a series of independent events, which means the outcome of one toss does not affect the outcome of the others. In this case, you are interested in the probability of heads on the fifth trial after obtaining heads four times in a row.
Since the outcome of the fifth trial is independent of the previous four, the probability of getting heads on the fifth trial remains unchanged. The probability of obtaining heads or tails when flipping a penny is always 0.5 (or 1/2) for each side, as there are only two possible outcomes.
Therefore, the correct answer is:
a. 0.5
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CAN SOMEONE HELP ME FIND THE SURFACE AREA
Answer:
Step-by-step explanation:
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
The statement about probability that is true is option The probability of landing on orange is equal to the probability of landing on yellow.
What is the probability?From the question, the spinner has:
8 sections, with:
1 orange section2 purple sections2 yellow sections3 blue sections.So probability of one getting on any section is = 1/8, or 0.125.
Therefore, the probability of getting on orange will still be the same as the probability of landing on yellow and as such option C is correct.
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Q1 ***Open Data1 Population average for social conservatism is M=5.40 Effect size for the variable of social conservatism is d = 0.4 2) Is your data normally distributed? Report. 4p
We need additional information, such as a dataset or summary statistics to perform a normality test.
To determine if the data is normally distributed, we need to look at the distribution of the variable of interest. In this case, we are interested in the distribution of social conservatism scores.
If we have access to the data, we can use statistical tests such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test to determine if the data is normally distributed. However, since we only have information about the population average and effect size, we cannot directly test for normality.
However, based on the central limit theorem, we can assume that if the sample size is large enough (typically >30), the distribution of the variable of interest will be approximately normal. In this case, since we do not have information about the sample size, we cannot definitively say if the data is normally distributed.
In summary, without more information about the sample size or access to the data, we cannot determine if the data is normally distributed.
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Statistics from the Port Authority of New York and New Jersey show that 80% of the vehicles using the Lincoln Tunne that connects Now York City and New Jersey use ZPass to pay the toll rather than stopping at a toll booth: Twelve cars are randomiy ected: Click here for the Excel Data File How many of the 12 vehicle would You expect - use E-ZPass? (Round your answer to decimal places ) Numoer vehickus What the mode of the distribution? What probability associated with the mode? (Round your answer to declmal places } HIcbe Probabilit of the sampled vehicles use E-ZPass? (Round your answer to decimal places ) probability four more What E Orcnabilih
We can find that this probability is 0.99994, rounded to five decimal places.
Based on the given statistic, we know that 80% of vehicles using the Lincoln Tunnel use E-ZPass. Therefore, we can expect that out of the 12 randomly selected vehicles, 80% or 0.8 * 12 = 9.6 vehicles would use E-ZPass. Rounding to the nearest whole number, we would expect 10 of the 12 vehicles to use E-ZPass.
The mode of the distribution is 10, as this is the most frequently occurring value in the sample.
Since 10 out of 12 vehicles is the mode, the probability associated with the mode is the proportion of vehicles that use E-ZPass in the sample. Therefore, the probability associated with the mode is 10/12 or 0.833, rounded to three decimal places.
The probability of four or more vehicles using E-ZPass can be calculated using the binomial distribution. The probability of a single vehicle using E-ZPass is 0.8, and the probability of a single vehicle not using E-ZPass is 0.2. The probability of four or more vehicles using E-ZPass is the sum of the probabilities of selecting 4, 5, 6, 7, 8, 9, 10, 11, or 12 vehicles that use E-ZPass. Using Excel or a calculator, we can find that this probability is 0.99994, rounded to five decimal places.
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