Answer:
a) 25.46% of tablets will contain less than 104 mg of the active chemical.
b) 0.52% of samples will have a sample mean of less than 104 mg of the active chemical.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Normal distribution with mean 105 mg and standard deviation 1.513 mg.
This means that [tex]\mu = 105, \sigma = 1.513[/tex]
A) Calculate the percentage of tablets that will contain less than 104 mg of the active chemical.
The proportion is the pvalue of Z when X = 104. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{104 - 105}{1.513}[/tex]
[tex]Z = -0.66[/tex]
[tex]Z = -0.66[/tex] has a pvalue of 0.2546
0.2545*100 = 25.46
25.46% of tablets will contain less than 104 mg of the active chemical.
B) Suppose samples of 15 randomly selected tablets are taken and the amount of active chemical measured. Calculate the percentage of samples that will have a sample mean of less than 104 mg of the active chemical.
Sample means from samples of 15. So, by the Central Limit Theorem:
[tex]n = 15, s = \frac{1.513}{\sqrt{15}} = 0.39[/tex]
The proportion is the pvalue of Z when X = 104. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{104 - 105}{0.39}[/tex]
[tex]Z = -2.56[/tex]
[tex]Z = -2.56[/tex] has a pvalue of 0.0052
0.0052*100 = 0.52
0.52% of samples will have a sample mean of less than 104 mg of the active chemical.
ANOTHER PI DAY QUESTION! LAST ONE!
Pi belongs to which number set?
I would say it would be irrational because PI is said to never end, but it won't take my answer. Any other ideas?
Answer:
I would try saying that it is a real number
Step-by-step explanation:
Answer:
Pi is a Real or Complex number
12. Elmo is standing on a parade float tossing candy out to everyone. The candy is thrown with a starting velocity of 10
feet per second from a height of 3 feet modeled by the equation: h= -16t2 + 10t + 3
After how many seconds will the ball be 2 feet in the air?
a. 0.125
b. 0.5
c. 0.71
d. 0.625
Answer:
c. 0.71
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
The height of the candy after t seconds is given by the following equation:
[tex]h(t) = -16t^2 + 10t + 3[/tex]
After how many seconds will the ball be 2 feet in the air?
This is t for which [tex]h(t) = 2[/tex]
So
[tex]h(t) = -16t^2 + 10t + 3[/tex]
[tex]2 = -16t^2 + 10t + 3[/tex]
[tex]-16t^2 + 10t + 1 = 0[/tex]
So
[tex]a = -16, b = 10, c = 1[/tex]
[tex]\Delta = b^{2} - 4ac = 10^2 -4(-16)(1) = 164[/tex]
[tex]t_{1} = \frac{-10 + \sqrt{164}}{2*(-16)} = -0.09[/tex]
[tex]t_{2} = \frac{-10 - \sqrt{164}}{2*(-16)} = 0.71[/tex]
Since time is a positive measure, the answer is 0.71, which is option c.
Find the solution set.
The solution set for 512 - 125 = 0 is
Answer:
(-5,5)
Step-by-step explanation:
5v² - 125 = 0
5v² = 125
v² = 125 ÷ 5
v² = 25
v = √25
v = ±5
v = (-5,5)
hihhhhi someone help please ..
Answer:
1. 2³
2.2⁵= 2×2×2×2×2= 32
2⁶= 2×2×2×2×2×2= 64
Step-by-step explanation:
hope it helps
Answer:
1. [tex]2^{3}[/tex]
2. It represents [tex]2*2*2*2*2[/tex] and [tex]2*2*2*2*2*2[/tex]
Step-by-step explanation:
1. it would have to be an exponent so 2*2*2 is 8 and 2^3 is also 8
2. it is an exponent so it would basically be multiplying the number times the number/amount of exponents so 2^5= 32 and 2^6=64
hope this helped :)
Stable cost reporting in a manufacturing setting is typically a sign that operations are running smoothly. The accounting department at Rockwell Collins, an avionics manufacturer, analyzes the variance of the weekly costs reported by two of its production departments. A sample of 16 cost reports for each of the two departments shows cost variances of 2.3 and 5.4, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance? Use α = 0.10 (to 2 decimals).
Answer:
Following are the responces to the given question:
Step-by-step explanation:
For this issue the statistical programme performance is:
Two overview hypothesis test sample variance:
[tex]\to \sigma_1^2[/tex] =Population variance 1
[tex]\to \sigma_2^2[/tex] = Population variance 2
[tex]\to \frac{\sigma_1^2}{\sigma_2^2}=[/tex] Two variance ratios
[tex]\to H_0: \frac{\sigma_1^2}{\sigma_1^2}=1\\\\\to H_A: \frac{\sigma_1^2}{\sigma_1^2}\neq 1[/tex]
Following are the result of the Hypothesis test: [tex]Ratio \ \ \ \ \ \ \ \ \ \ Num.DF \ \ \ \ \ \ \ \ \ \ Den.DF \ \ \ \ \ \ \ \ \ Sample\ \ Ratio\ \ \ \ \ \ F-Stat \ \ \ \ \ \ \ P-value\\\\[/tex]
[tex]\frac{\sigma_1^2}{\sigma_1^2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 15 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 15 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.3478261 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.3478261 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1091[/tex]
Test statistic [tex]= 2.3478 \approx 2.35[/tex]
P-value > 0.10
The null hypothesis should not be rejected.
Find the slope of the line (-2,3) (2,-3)
An element with mass 510 grams decays by 26.3% per minute. How much of the element is remaining after 7 minutes, ?
Answer: The element is remaining after 7 minutes = 60.23 grams
Step-by-step explanation:
The equation for mass decay :
[tex]A=A_0(1-r)^t[/tex], where [tex]A_0[/tex] = initial mass, A = mass after t minutes.
Given: [tex]A_0=510\ grams[/tex]
r = 26.3% = 0.263
t = 7 minutes
[tex]A=510(1-0.263)^7\\\\=510(0.737)^7\\\\=510(0.118106123435)\approx60.23\ grams[/tex]
Hence, the element is remaining after 7 minutes = 60.23 grams
Answer:
Its the sames steps as the other answer but round the decimal instead of 60.23 do 60.2 because the ,23 is rounded to the nearest 10th i think thats how i got it right
Step-by-step explanation:
Maria bought a bag of mixed fruit that is 40% oranges, 33% green apples, and 27% red apples, If she
randomly selects 5 pieces of fruit from the
bag, how many would you expect to be oranges?
A 1
B 2
C 3
D 4
Answer:
b
Step-by-step explanation:
Find the angle x, between the tops of two steel beams in front and on top of the building. Round your answer to the nearest tenth if needed.
Answer:
55 Degrees
Step-by-step explanation:
Choose the equation for the line in slope-intercept form.
please hurry and answer
Answer:
(d). 6Step-by-step explanation:
(6)² = 5(6) + 6
36 = 30 + 6
36 = 36
Hence, the right answer is 6.You randomly select ONE card from a 52-card deck. Find the probability of selecting a card greater than 2 and less than 7, or a diamond.
There is 13 diamonds and 4 numbers greater than 2 but less than 7. This means your probability of selecting one of these specific cards is a 17/52 chance
For my friend I’ll mark you and thanks you
Maitland multiplies 0.05 x 0.8 on a calculator. The calculator shows a product of 0.04. Maitland says the calculator must be broken because multiplying tenths by hundredths give a product in the thousandths.
Is the calculator broken?
Answer:
no, the calculator is not broken
Step-by-step explanation:
its not broken i got the same answer your welcome
I need help with this
9514 1404 393
Answer:
vertical shrink by a factor of 1/3shift right 2 unitsshift down 4 unitsStep-by-step explanation:
The transformations of interest here are ...
g(x) = k·f(x) . . . . . vertically scale f(x) by a factor of k
g(x) = f(x -h) . . . . shift f(x) right by h units
g(x) = f(x) +k . . . . shift f(x) up by k units
__
Working left to right, the first factor we encounter is 1/3, multiplying the value that is cubed. This means the vertical scale factor of f(x) = x^3 is 1/3. A scale factor less than 1 represents a shrink, so ...
transformation #1 = shrink by a factor of 1/3
The next number we encounter is -2 in the factor (x -2)^3. This means h=2 in f(x -h) = (x -2)^3. The horizontal shift right is 2 units:
transformation #2 = right shift 2 units
Finally, we encounter the number -4. This means k=-4 in g(x)=f(x)+k. The up-shift is negative, so ...
transformation #3 = shift down 4 units
__
The right- and down-shifts can be done in either order. Here, we have done them as we see them when scanning the equation left-to-right. The vertical scaling must be done before the down-shift, so that it does not affect the amount of down-shift.
The difference between 13 and a number k in algebraic expression?
i need help with this problem
9514 1404 393
Answer:
(a) 4 in²
Step-by-step explanation:
The volume of a rectangular prism is given by the formula ...
V = Bh
where B is the area of the base, and h is the height of the prism.
We can find the area of the base by solving for B.
B = V/h
B = (12 in³)/(3 in)
B = 4 in² . . . . . . . . . . matches the first choice
What is the value of x to the nearest tenth?
37°
2.1
Answer: 2.1 tan 37 = x/2.1 * 2.1. 2.1 tan 37 = x. 1.582463505 =x. To the nearest tenth. 1.6 =x.
Step-by-step explanation:
PSSS I REALLY NEED HELP
Answer:
x=7.45
Step-by-step explanation:
Hey There!
For this one we are going to solve for x using trigonometry
Law of Sines to be more specific
So basically [tex]\frac{7}{sin(70)} = \frac{x}{sin(90)}[/tex]
Step on multiply each side by sin(90)
now we have
[tex]x=\frac{7*sin(90)}{sin(70)}[/tex]
7*sin90=7
[tex]\frac{7}{sin70} =7.4492944407[/tex]
Then we just round to the nearest hundredth which would make it into 7.45
Therefore x=7.45
You go to Giant to buy some candy. You decide to buy snickers because they have a special deal on snickers. A pound of snickers costs $3.45, but if you buy 4 or more pounds, they only cost $3.00per bag. Write a piecewise function to represent this situation.
Answer:
y = x*$3.45 if 0 ≤ x < 4
y = x*$3.00 if 4 ≤ x
Step-by-step explanation:
A piecewise function is a function that behaves differently in diferent intervals of it's domain.
We know that 1lb of candy costs $3.45
But if you buy 4 lb or more, the cost of each lb is $3.00
Then if x represents the number of pounds of candy that you buy, we have the equation:
y = x*$3.45 if 0 ≤ x < 4
y = x*$3.00 if 4 ≤ x
(a)
Joanna earns $12 per hour at her job. Last week, Joanna earned $432.
Part A
Which equation can be used to determine the number of hours Joanna worked last week?
Part B
What is the number of hours Joanna worked last week?
Answer
432 divided by 12
she worked 32 hours
Step-by-step explanation:
There are 37 students on a bus the bus stops 5 times. 7 students get off at each stop how many students are left on the bus
Which of the following uses scientific notation
incorrectly?
(View picture)
300 college students were surveyed on the number of study hours they spend each week.
The results of a sample of 7 students are given in the following table:
Study Hours:
4
10
20
24
34
36
42
Z Score:
- 2.5 - 1.75
- 0.5
0
1.25
1.5
2.25
Percentile Rank:
10
25
35
40
50
75
95
By Inspection, answer the questions in GH2
Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!
tinyurl.com/wpazsebu
4x+2-x=17
Solve the equation for x
Explain how
Answer:
5
Step-by-step explanation:
4x-x=17-2
3x=15I:3
x=5
i think thats right
3(4x + 10) = 12x + 20
How many solutions does this equation have ?
please help me.. i would really appreciate it, thank you!
The measure of angle A is 68°. The measure of angle B is 22°. Which statement best describes the relationship between these two angles?
Answer:
They are complementary angles.
Step-by-step explanation:
The sum of their measurements equals 90 degrees.
4x + 3 − 23x
This expression has 3 terms.
true or false
Answer:
True
Terms are separated by the signs
It says First,show 3/5 of 1/4 on the model. I don't know how pls help me.
Answer:3/20
Step-by-step explanation: