Answer:
a) 0.048 = 4.8% probability of exactly seven successes.
b) 100% probability of at least twenty-two successes.
Step-by-step explanation:
The first question we use the binomial distribution, while for the second we use the approximation to the normal.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Question a:
Here, we have [tex]n = 10, p = 0.41[/tex].
This probability is P(X = 7). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{10,7}.(0.41)^{7}.(0.59)^{3} = 0.048[/tex]
0.048 = 4.8% probability of exactly seven successes.
b) With 150 trials and a 39 chance of success, the probability of at least twenty-two successes.
Here we have [tex]n = 150, p = 0.39[/tex]
Mean and standard deviation:
[tex]\mu = 150*0.39 = 58.5[/tex]
[tex]\sigma = \sqrt{150*0.39*0.61} = 5.9737[/tex]
This probability is, using continuity correction, [tex]P(X \geq 22 - 0.5) = P(X \geq 21.5)[/tex], which is 1 subtracted by the p-value of Z when X = 21.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21.5 - 58.5}{5.9737}[/tex]
[tex]Z = -6.19[/tex]
[tex]Z = -6.19[/tex] has a p-value of 0
1 - 0 = 1
100% probability of at least twenty-two successes.
Kevin's bedroom is 14 feet long and
10 feet wide.
His bathroom is the half the length and half
the width of his bedroom. How do
the areas of these two rooms
compare?
Answer:
bathroom area is 1/4 area of bedroom
Step-by-step explanation:
bathroom area = 35 sq ft
bedroom area = 140 sq ft
The circumference of a circle is 119.32 centimeters. What is the circle's diameter?
Use 3.14
c=2πr
119.32=2πr
119.32=2*3.14r
119.32/(2*3.14)=r
r=19
d=2r
d=2*19
ANSWER: d=38cm
Find the area of the shaded figure. Give answer in decimal to the hundredth place.
Answer:
13.5
Step-by-step explanation:
72/(16/3)
one antifreeze solution is 41% alcohol and another is 24% alcohol. how much of each mixture should be added to make 51 l of a solution that is 35% alcohol.
Write your Answer here please i need this please
Answer:
A
Step-by-step explanation:
300-50-70+20
Answer:
I believe it would be answer A.
Step-by-step explanation:
When depositing, you're make an addition. Withdrawing, is removing. Making these checks had removed about 120 dollars out of his bank account, meaning the equation would be 300-50-70+20.
Hope this helps! :D
HELPPPPPPPP!!!!!!!!!!! Pleaseeeeeee!!!!!!!
Answer:
C
Step-by-step explanation:
Sorry if this is wrong.
Hi can someone answer this question please
Which number line represents the solution to the inequality -7x - 13 ≥ 87
Answer:
x ≤ - 3
Option A
Step-by-step explanation:
Given the inequality :
-7x - 13 ≥ 8
Add 13 to both. Sides
-7x - 13 + 13 ≥ 8 + 13
-7x ≥ 21
Divide both sides by -7
x ≤ - 3
The diameter of a circle is 12 miles, what is the length of the 180 degree arc in the simplest form?
9514 1404 393
Answer:
6π ≈ 18.8 miles
Step-by-step explanation:
The full circumference of a 12-mile circle is ...
C = πd
C = π(12 mi)
So, half the circumference of the circle is ...
arc length = 1/2C = (12π mi)/2 = 6π mi ≈ 18.8 mi
The following are house prices in Southern California:
$750,000 $875,000 $800,000 $700,000 $1,000,000 $1, 160,000 $1, 180,000
What is the median house price?
A. $875, 000
B. $1,000,000
C. $700,000
D. $923,000
Answer:
A. 875,000
Step-by-step explanation:
Order them by least to greatest and then find the median from there so, 700,000; 750,000; 800,000; 875,000; 1,000,000; 1,160,000; 1,180,000
875,000 is the middle man so there is your answer
PLEASE! TEST QUESTION
Jenelle invested $17000 in two mutual funds. Fund A earned 4% profit during the first year, while Fund B suffered a 1.5% loss. If she received a total of $460 profit, how much had she invested in each mutual fund?
Jenelle invested $_____ into Fund A.
Jenelle invested $_____ into Fund B.
Answer:
Jenelle invested $ 13,000 in Fund A and $ 4,000 in Fund B.
Step-by-step explanation:
Given that Jenelle invested $ 17000 in two mutual funds, and Fund A earned 4% profit during the first year, while Fund B suffered a 1.5% loss, if she received a total of $ 460 profit, to determine how much had she invested in each mutual fund, the following calculation must be performed:
17000 x 0.04 - 0 x 0.015 = 680
15000 x 0.04 - 2000 x 0.015 = 570
10,000 x 0.04 - 7000 x 0.015 = 295
12500 x 0.04 - 4500 x 0.015 = 432.5
13000 x 0.04 - 4000 x 0.015 = 460
Therefore, Jenelle invested $ 13,000 in Fund A and $ 4,000 in Fund B.
Probability distribution
Answer:
a) The value of q is 0.2.
b) E(X) = 1.85.
Step-by-step explanation:
Question a:
The sum of all the probabilities must be 1. So
[tex]0.3 + x + 0.1 + 0.15 + 0.25 = 1[/tex]
[tex]x + 0.8 = 1[/tex]
[tex]x = 0.2[/tex]
The value of q is 0.2.
Question b:
Multiplication of each value of x by its probability. So
[tex]E(X) = 0*0.3 + 1*0.2 + 2*0.1 + 3*0.15 + 4*0.25 = 1.85[/tex]
So the answer is E(X) = 1.85.
Find the value of x.
Plsss help me, i need to round to the nearest angle:)
Help on this question please!!
Answer:
[tex]y' = (6,4)[/tex]
Step-by-step explanation:
Given
[tex]y = (3,2)[/tex]
[tex]x = (4,0)[/tex]
[tex]z = (2,-2)[/tex]
[tex]D_{(O,2)}[/tex]
Required
The image of y
[tex]D_{(O,2)}[/tex] implies that y is dilated by a scale factor of 2 across the origin.
So, the image of y is:
[tex]y' = 2 * y[/tex]
[tex]y' = 2 * (3,2)[/tex]
[tex]y' = (6,4)[/tex]
1.
A diagram of Ryan's yard is shown.
-12 ft
10 ft
14 ft
5 ft
Which expression can Ryan use to find the total
area of his yard?
A. (10+4)(12+5)
B
(10 + 4) X (12 - 5)
C. (12 x 10) - (5 x 4)
D. (12 x 10) + (5 x 4)
Answer:
D. (12 x 10) + (5 x 4)
Step-by-step explanation:
If you draw a line separating the big square from the little square, you have a 12 x 10 large square, and a 5 x 4 smaller square. We know the second dimension of the small square because the large square takes 10ft off of the total length of 4ft.
Calculate both areas separately, then add them together.
Please help me with this guys
Answer:
reflection across the x axis then reflection across the y axis
Step-by-step explanation:
A population has a standard deviation of 24. What is the standard error of the sampling distribution if the sample size is 100?
A. 0.48
B. 4.8
C. 0.24
D. 2.4
Answer:
D. 2.4.
Step-by-step explanation:
S.E. = std dev / √N
= 24 / √100
= 2.4.
The standard error of the sampling distribution will be 2.4. Then the correct option is D.
The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, constitutes the statistic's measurement error (SE).
SE = σ / √n
A population has a standard deviation of 24. Then the standard error of the sampling distribution, if the sample size is 100, is calculated as,
SE = σ / √n
SE = 24 / √100
SE = 24 / 10
SE = 2.4
The standard error of the sampling distribution will be 2.4. Then the correct option is D.
More about the standard error link is given below.
https://brainly.com/question/13179711
#SPJ3
isaac invested $77,000 in an account paying interest rate of 4.6% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be the count after 12 years?
Answer:
$133,728 would be in the count after 12 hours.
Step-by-step explanation:
Continuous compounding:
The amount of money, in continuous compounding, after t years, is given by:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial deposit and r is the interest rate, as a decimal.
Isaac invested $77,000 in an account paying interest rate of 4.6% compounded continuously.
This means that [tex]P(0) = 77000, r = 0.046[/tex]
Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be the count after 12 years?
This is P(12). So
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]P(12) = 77000e^{0.046*12} = 133728[/tex]
$133,728 would be in the count after 12 hours.
Anne, Barry, and Cathy enter a coffee shop. Anne orders two coffees, one juice, and two doughnuts and pays $7.50. Barry orders one coffee and three doughnuts and pays $5.00. Cathy orders three coffees, one juice, and four doughnuts and pays $11.50. Find the price of coffee, juice, and doughnuts at this coffee shop.
Answer:
Coffee = $2.00
Juice = $1.50
Doughnut = $1.00
Step-by-step explanation:
Given
Let:
[tex]c = coffee\\ j= juice\\ d = doughnut[/tex]
So, we have:
Anna
[tex]2c + j + 2d = 7.50[/tex]
Barry
[tex]c + 3d = 5.00[/tex]
Cathy
[tex]3c + j + 4d = 11.50[/tex]
Required
The price of each
We have:
[tex]2c + j + 2d = 7.50[/tex]
[tex]c + 3d = 5.00[/tex]
[tex]3c + j + 4d = 11.50[/tex]
Make c the subject in: [tex]c + 3d = 5.00[/tex]
[tex]c = 5.00 - 3d[/tex]
Substitute [tex]c = 5.00 - 3d[/tex] in [tex]2c + j + 2d = 7.50[/tex] and [tex]3c + j + 4d = 11.50[/tex]
[tex]2c + j + 2d = 7.50[/tex]
[tex]2[5.00 - 3d] + j + 2d = 7.50[/tex]
[tex]10.00 - 6d+ j + 2d = 7.50[/tex]
Make j the subject
[tex]j = 7.50 - 10.0 +6d - 2d[/tex]
[tex]j = -2.50 +4d[/tex]
[tex]3c + j + 4d = 11.50[/tex]
[tex]3[5.00 - 3d] + j + 4d = 11.50[/tex]
[tex]15.00 - 9d + j + 4d = 11.50[/tex]
Make j the subject
[tex]j = 11.50 - 15.00 + 9d -4d[/tex]
[tex]j = -3.50 + 5d[/tex]
So, we have:
[tex]j = -3.50 + 5d[/tex] and [tex]j = -2.50 +4d[/tex]
Equate both values of j
[tex]-3.50 + 5d = -2.50 + 4d[/tex]
Collect like terms
[tex]5d - 4d = 3.50 -2.50[/tex]
[tex]d = 1.00[/tex]
Substitute [tex]d = 1.00[/tex] in [tex]j = -3.50 + 5d[/tex]
[tex]j = -3.50 + 5d[/tex]
[tex]j = -3.50 + 5 * 1.00[/tex]
[tex]j = -3.50 + 5.00[/tex]
[tex]j = 1.50[/tex]
To solve for c, we substitute [tex]d = 1.00[/tex] in [tex]c + 3d = 5.00[/tex]
[tex]c + 3 * 1.00 =5.00[/tex]
[tex]c + 3.00 =5.00[/tex]
Solve for c
[tex]c =- 3.00 +5.00[/tex]
[tex]c =2.00[/tex]
Solve for x.
5x - 6 = 4x + 8
Ox=-14
Ox=-2
Ox= 14
Ox=2
Answer: c is your answer hope this helped
plz make brainly
Step-by-step explanation:
Find the complete factored form of the
polynomial:
- m2n5 - 4m3n6
Enter the correct answer.
Answer:
-m^2n^5(1+4mn)
If the expression below has a positive value, which inequality represents all possible values of x in the expression? -3x
Answer:
x < 0
Explanation:
A negative times a negative equals a positive, and the expression is positive, so x has to be negative/less than 0
I know you already got the answer, but one of the links was deleted so I thought I'd post it as an answer instead of a comment :)
You have 24 seashells and give 8 seashells to your sister. You arrange the rest of the seashells into 4 equal rows. Which steps can you use to find the number of seashells in each row?
Step 1: 24 – 8 = 16
Step 2: 16 × 4 = 64
There are 64 seashells in each row.
Step 1: 24 – 8 = 16
Step 2: 16 ÷ 4 = 4
There are 4 seashells in each row.
Step 1: 24 + 8 = 32
Step 2: 32 ÷ 4 = 8
There are 8 seashells in each row.
Step 1: 8 ÷ 4 = 2
Step 2: 24 – 2 = 22
There are 22 seashells in each row.
Answer:
I'm sorry dont leave me I need you here with me now
I'm sorry that are love is gone the love is gone☹☹
Questlon 2 of 10 Which distribution is positively skewed? will give brainliest
Answer:
The answer is B
Step-by-step explanation:
Four classmates collect data by conducting a poll. They
ask students chosen at random how many days a week
they usually have homework.
.
Taylor interviews 30 students.
.
Hunter interviews 40 students.
• Grace interviews 20 students.
.
Aidan interviews 70 students.
Whose results are probably the most trustworthy?
A. Taylor's
B. Grace's
C. Hunter's
D. Aidan's
A brick has a mass of 18.3 kg and a volume of 890 cm3.
Evaluate the density of the brick in g/cm3 rounded to 3 significant figures.
1 g/cm3
Answer
Calculate Volume ... the length and mass measurements all had 3 significant figures.
Step-by-step explanation:
G O O G L E
I need the answer fast pls
Answer:
C. A = 0.5*d1*d2
D. A = bh
Step-by-step explanation:
The area of the rhombus can be found depending on what information is made available to us.
If given the lengths of the two diagonals (d1 and d2) of a rhombus which bisect each other, therefore, the formula for finding the area would be:
A = 0.5*d1*d2
Also, if we are given the height (h) and side (b), the formula to use would be:
A = bh
Plz answer this question need ASAP
Answer
its b
Step-by-step explanation:
43k 67u 88j
Use a ratio box to solve this problem. The price of one model of car increased 10 percent in one year. If the price this year is $17,600,
what was the price last year
Answer:
$15,840
Step-by-step explanation:
10% of 17600 = 1760
17600 - 1760 = 15840
Can anyone help? I’ll give Brainly! Thank you :)
Answer:
(p)60/100 :)
Step-by-step explanation:
Answer:
[tex]1-\frac{2+13+25}{100} = 0,6[/tex]