Mathematics, 10.10.2019 22:00 scottbrandon653

The economic policy institute periodically issues reports on wages of entry level workers. the institute reported that entry level wages for male college graduates were $21.68 per hour and for female college graduates were $18.80 per hour in 2011 (economic policy institute website, march 30, 2012). assume the standard deviation for male graduates is $2.30, and for female graduates it is $2.05 what is the probability that a sample of 50 male graduates will provide a sample mean within $.50 of the population mean, $21.68?

what is the probability that a sample of 50 female graduates will provide a sample mean within $.50 of the population mean, $18.80?

what is the probability that a sample of 120 female graduates will provide a sample mean more than $.30 below the population mean?

Answers: 2

Show answers

Answers

Answer from: macycj8

87.64% probability that a sample of 50 male graduates will provide a sample mean within $.50 of the population mean, $21.68.

91.46% probability that a sample of 50 female graduates will provide a sample mean within $.50 of the population mean, $18.80.

5.48% probability that a sample of 120 female graduates will provide a sample mean more than $.30 below the population mean.

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 $\frac{\sigma}{\sqrt{n}}$ .

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.

So, lets see each question:

What is the probability that a sample of 50 male graduates will provide a sample mean within $.50 of the population mean, $21.68?

The Institute reported that entry level wages for male college graduates were $21.68 per hour, with a standard deviation of 2.30.

So $\mu = 21.68, \sigma = 2.30, n = 50, s = \frac{2.30}{\sqrt{50}} = 0.3253$

This probability is the pvalue of Z when X = 21.68 + 0.50 = 22.18 subtracted by the pvalue of Z when X = 21.68 - 0.50 = 21.18

X = 22.18

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

$Z = \frac{22.18 - 21.68}{0.3253}$

Z = 1.54

Z = 1.54 has a pvalue of 0.9382.

X = 21.18

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

$Z = \frac{21.18 - 21.68}{0.3253}$

Z = -1.54

Z = -1.54 has a pvalue of 0.0618.

There is a 0.9382 - 0.0618 = 0.8764 = 87.64% probability that a sample of 50 male graduates will provide a sample mean within $.50 of the population mean, $21.68.

What is the probability that a sample of 50 female graduates will provide a sample mean within $.50 of the population mean, $18.80?

$\mu = 18.80, \sigma = 2.05, n = 50, s = \frac{2.05}{\sqrt{50}} = 0.29$

This probability is the pvalue of $Z = \frac{0.50}{0.29} = 1.72$ subtracted by the pvalue of $Z = -\frac{0.50}{0.29} = -1.72$ , following the same logic as the question above.

There is a 0.9573 - 0.0427 = 0.9146 = 91.46% probability that a sample of 50 female graduates will provide a sample mean within $.50 of the population mean, $18.80.

What is the probability that a sample of 120 female graduates will provide a sample mean more than $.30 below the population mean?

$\mu = 18.80, \sigma = 2.05, n = 120, s = \frac{2.05}{\sqrt{120}} = 0.1871$

This is the pvalue of Z when X = 18.80 - 0.30 = 18.50

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

$Z = \frac{18.50 - 18.80}{0.1871}$

Z = - 1.6

Z = - 1.6 has a pvalue of 0.0548.

So there is a 5.48% probability that a sample of 120 female graduates will provide a sample mean more than $.30 below the population mean.

Answer from: Quest

been looking for the answer havent been able to find it but good luck with it

Answer from: Quest

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175

Another question on Mathematics

Mathematics, 20.06.2019 18:04

If f(x)=2x^6+x^2+2 then what is the remainder when f(x)is divided by x+2

Answers: 1

Answer

Mathematics, 21.06.2019 18:00

What set does not contain -3 the set of all real numbers the set of all integers the set of all whole numbers the set of all rational numbers

Answers: 1

Answer

Mathematics, 22.06.2019 00:30

Answer 20 points and brainiest ! on the board, your teacher writes an example of how to find the median. one of the numbers is erased, leaving what is shown, 18, 30, 26,12 22. what is the median? a. 10 b. 20 c. 24 d. 28

Answers: 1

Answer

Mathematics, 22.06.2019 03:30

Breana is selling tickets to a choral performance. on the first day of ticket sales , she sold 3 senior citizen tickets and 1 child ticket for a total of $38. breana took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. what is the price of a senior citizen ticket?

Answers: 1

Answer

You know the right answer?

The economic policy institute periodically issues reports on wages of entry level workers. the insti...

Questions