Mathematics, 16.03.2020 21:57 maribel234

BusinessWeek conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation for the male graduates is $40,000, and for the female graduates it is $25,000. What is the probability that a simple random sample of 40 male graduates will provide a sample mean within $10,000 of the population mean, $168,000

Answers: 2

Show answers

Answers

Answer from: Alangs

88.58% probability that a simple random sample of 40 male graduates will provide a sample mean within $10,000 of the population mean, $168,000

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are 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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 168000, \sigma = 40000, n = 40, s = \frac{40000}{\sqrt{40}} = 6324.55$

What is the probability that a simple random sample of 40 male graduates will provide a sample mean within $10,000 of the population mean, $168,000

This is the pvalue of Z when X = 168,000 + 10,000 = 178,000 subtracted by the pvalue of Z when X = 168,000 - 10,000 = 158,000. So

Z = 178000

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

By the Central Limit Theorem

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

$Z = \frac{178000 - 168000}{6324.55}$

Z = 1.58

Z = 1.58 has a pvalue of 0.9429

Z = 158000

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

$Z = \frac{158000 - 168000}{6324.55}$

Z = -1.58

Z = -1.58 has a pvalue of 0.0571

0.9429 - 0.0571 = 0.8858

88.58% probability that a simple random sample of 40 male graduates will provide a sample mean within $10,000 of the population mean, $168,000

Answer from: Quest

step-by-step explanation:

6 (donuts) divided by 3 is 2.

so 2/3 means 2 times 2, which is 4/6.

you get two and your friend gets four.

Answer from: Quest

idk

cfgghbjn bvcdftfghjnbgvfcdrtrfytgyuhuji

Problem 33 is shown in the diagram. why is the answer to this question not a but d

Another question on Mathematics

Mathematics, 21.06.2019 17:30

43lbs of tomatos cost $387. how much would 41lbs cost

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

An account with a $250 balance accrues 2% annually. if no deposits or withdrawals are made, which graph can be used to determine approximately how many years will it take for the balance to be $282? it's e2020 ni️️as

Answers: 1

Answer

Mathematics, 21.06.2019 22:00

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.

Answers: 2

Answer

Mathematics, 22.06.2019 01:00

Sanderson is having trouble with his assignment. his shown work is as follows: − 3 7 7 3 = − 3 7 × 7 3 = − 21 21 = −1 however, his answer does not match the answer that his teacher gives him. complete the description of sanderson's mistake. find the correct answer.

Answers: 3

Answer

You know the right answer?

BusinessWeek conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, a...

Questions