1. Suppose the heights of 18-year-old men are approximatelynormally distributed, with mean71inches and standard deviation2inches.(a) What is the probability that an 18-year-old man selected at random is between70and72inches tall? (Round your answer to four decimal places.)

.3829

(b) If a random sample oftwenty-eight18-year-old men is selected, what is the probability that the mean heightis between70and72inches? (Round your answer to four decimal places.)

.9918

(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

a. The probability in part (b) is much higher because the standard deviation is smaller for thedistribution. b. The probability in part (b) is much higher because the standard deviation is larger for thedistribution. c. The probability in part (b) is much lower because the standard deviation is smaller for thedistribution. d. The probability in part (b) is much higher because the mean is smaller for thedistribution. e. The probability in part (b) is much higher because the mean is larger for thedistribution.

2. Assume thatxhas a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)=38;=15 P(50x70) =

3.Assume thatxhas a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)=49;=13 P(40x47) =

4.Lorraine computed a confidence interval forbased on a sample of size 41. Since she did not know, she usedsin her calculations. Lorraine used the normal distribution for the confidence interval instead of a Student'stdistribution. Will her interval be longer or shorter than one obtained by using an appropriate Student'stdistribution? Explain.

a. Longer. Ford.f.= 40,z_cis greater thant_c.

b. Shorter. Ford.f.= 40,z_cis greater thant_c.

c. Longer. Ford.f.= 40,z_cis less thant_c.

d. Shorter. Ford.f.= 40,z_cis less thant_c.

5.How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from20Fto45F.A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population ofxvalues has an approximately normal distribution.

75	60	45	50	90	75	30	23	100	110
105	95	105	60	110	120	95	90	60	70

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean priceand sample standard deviations. (Round your answers to two decimal places.)

mean = $78.40	$
s= $27.98	$

(b) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean priceof all summer sleeping bags. (Round your answers to two decimal places.)

lower limit	$??
upper limit	$ ???

6.For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a survey of 1000 large corporations,252said that, given a choice between a job candidate who smokes and an equally qualified nonsmoker, the nonsmoker would get the job.(a) Letprepresent the proportion of all corporations preferring a nonsmoking candidate. Find a point estimate forp. (Round your answer to four decimal places.) .2520 (b) Find a 0.95 confidence interval forp. (Round your answers to three decimal places.)

lower limit	????????
upper limit	???????

(c) As a news writer, how would you report the survey results regarding the proportion of corporations that would hire the equally qualified nonsmoker? a.)Reportpalong with the margin of error.

b.)Report the margin of error.

c.Reportp.