Mathematics, 20.12.2019 19:31 eddsworldfrantic

When a production process is operating correctly, thenumber of units produced per hour has a normal distri- bution with a mean of 92.0 and a standard deviation of3.6. a random sample of 4 different hours was taken. a. find the mean of the sampling distribution of thesample means. b. find the variance of the sampling distribution ofthe sample mean. c. find the standard error of the sampling distribu-tion of the sample mean. d. what is the probability that the sample mean ex-ceeds 93.0 units?

Answers: 1

Show answers

Answers

Answer from: lulustar13

a) The mean of the sampling distribution of the sample means is 92.

b) The variance of the sampling distribution of the sample mean is 3.24.

c) The standard error of the sampling distribution of the sample mean is 1.8.

d) 28.77% probability that the sample mean ex-ceeds 93.0 units.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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.

In this problem, we have that:

$\mu = 92, \sigma = 3.6$ .

a. Find the mean of the sampling distribution of thesample means.

The mean is the same as the mean of the population. So the mean of the sampling distribution of the sample means is 92.

b. Find the variance of the sampling distribution ofthe sample mean.

The standard deviation is $s = \frac{\sigma}{\sqrt{n}} = \frac{3.6}{\sqrt{4}} = 1.8$

The variance is $s^{2} = 1.8^{2} = 3.24$

c. Find the standard error of the sampling distribution of the sample mean.

This is the same as the standard deviation of the sample. So the standard error of the sampling distribution of the sample mean is 1.8.

d. What is the probability that the sample mean ex-ceeds 93.0 units?

This is 1 subtracted by the pvalue of Z when X = 93. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{93 - 92}{1.8}$

Z = 0.56

Z = 0.56 has a pvalue of 0.7123.

So there is a 1-0.7123 = 0.2877 = 28.77% probability that the sample mean ex-ceeds 93.0 units.

Answer from: Quest

hello from mrbilldoesmath!

answer:

x - 3

discussion:

x^2 - 9 = (x-3) (x+3) so

(x^2-9)/ (x + 3) = x-3

you,

mrb

Answer from: Quest

1. 0.3 •4 is the same as 4 groups of 0.32. 7•0.8 is the same as 7 groups of 0.83. it increases by 0.5 every time, so 0.5x4 it increases by 0.9 every time, so 0.9x5. 0.9•12=10.86. 0.47•5=2.35i can finish the next ones in a separate post
Can someone plz me 1 to 37 . i will earn 10 points

Can someone plz me 1 to 37 . i will earn 10 points

Another question on Mathematics

Mathematics, 21.06.2019 21:00

Isabel graphed the following system of equations. 2x – y = 6 y = -3x + 4 she came up with the solution (2,-2). what were the 3 steps she did to get that solution? (make sure they are in the correct order)

Answers: 2

Answer

Mathematics, 21.06.2019 21:00

Acomposition of transformations maps δxyz to δx"y"z". the first transformation for this composition is , and the second transformation is a 90° rotation about point x'.

Answers: 1

Answer

Mathematics, 21.06.2019 21:50

Question 14 (1 point) larry deposits $15 a week into a savings account. his balance in his savings account grows by a constant percent rate.

Answers: 3

Answer

Mathematics, 22.06.2019 00:20

Three students, javier, sam, and corrine, participated in a fundraiser where people donated a certain amount of money per lap that the student ran. each student also had some initial donations that were collected before the run. the equations that represent each student's total donation, y, based on the number of laps ran, x, is shown below. match each equation with the correct rate of change for that student.

Answers: 1

Answer

You know the right answer?

When a production process is operating correctly, thenumber of units produced per hour has a normal...

Questions

Mathematics, 11.05.2021 21:40

Sarah has a bag of skittles, some are red and some are yellow. Sarah randomly pulls a skittle out the bag. So far, she has recorded 8 red and 12 yello...