Mathematics, 05.11.2019 05:31 vanessa7714102010

To estimate the mean height μ of male students on your campus, you will measure an srs of students. you know from government datathat heights of young men are approximately normal with standarddeviation about 2.8 inches. you want your sample mean x to estimateμ with an error of no more than one-half inch in eitherdirection.
(a) what standard deviation must x have so that 99.7% of allsamples give an x within one-half inch of μ?
(b) how large an srs do you need to reduce the standard deviationof x to the value you found in part (a)?

Answers: 2

Show answers

Answers

Answer from: Hilljos018

a) $\sigma = 0.167$

b) We need a sample of at least 282 young men.

Step-by-step explanation:

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

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

This Zscore is how many standard deviations the value of the measure X 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.

(a) What standard deviation must x have so that 99.7% of allsamples give an x within one-half inch of μ?

To solve this problem, we use the 68-95-99.7 rule. This rule states that:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we want 99.7% of all samples give X within one-half inch of $\mu$ . So $X - \mu = 0.5$ must have Z = 3 and $X - \mu = -0.5$ must have Z = -3 .

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

$3 = \frac{0.5}{\sigma}$

$3\sigma = 0.5$

$\sigma = \frac{0.5}{3}$

$\sigma = 0.167$

(b) How large an SRS do you need to reduce the standard deviationof x to the value you found in part (a)?

You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. This means that $\sigma = 2.8$

The standard deviation of a sample of n young man is given by the following formula

$s = \frac{\sigma}{\sqrt{n}}$

We want to have s = 0.167

$0.167 = \frac{2.8}{\sqrt{n}}$

$0.167\sqrt{n} = 2.8$

$\sqrt{n} = \frac{2.8}{0.167}$

$\sqrt{n} = 16.77$

$\sqrt{n}^{2} = 16.77^{2}$

n = 281.23

We need a sample of at least 282 young men.

Answer from: Quest

Look i don’t know the answer to this but someone else will so just wait a little bit longer

Answer from: Quest

The major difference is that a histogram is only used to plot the frequency of score occurrences in a continuous data set that has been divided into classes, called bins. bar charts, on the other hand, can be used for a great deal of other types ofvariables including ordinal andnominal data sets.

Another question on Mathematics

Mathematics, 21.06.2019 16:30

Which approach to the theory-and-research cycle does the following sequence reflect: (1) specific observations suggest generalizations, (2) generalizations produce a tentative theory, (3) the theory is tested through the formation of hypotheses, and (4) hypotheses may provide suggestions for additional observations?

Answers: 1

Answer

Mathematics, 21.06.2019 18:00

1. a parachutist is 800 feet above the ground when she opens her parachute. she then falls at a constant rate of 5 feet per second. select the equation that represents this situation. h = -800t + 5 y = -5x + 800 h = 5t - 800 y = 800x + 5 i need

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

Suppose that one doll house uses the 1 inch scale, meaning that 1 inch on the doll house corresponds to 1/2 foot for life-sized objects. if the doll house is 108 inches wide, what is the width of the full-sized house that it's modeled after? in inches and feet.

Answers: 2

Answer

Mathematics, 21.06.2019 20:00

Do,h = (7, 9) (14, 18) the scale factor is

Answers: 1

Answer

You know the right answer?

To estimate the mean height μ of male students on your campus, you will measure an srs of students....

Questions