Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard deviation 5 inches. (a) What is the probability that an 18-year-old man selected at random is between 68 and 70 inches tall? (Round your answer to four decimal places.) a 0.0793 b 0.1585     c 0.0317 d 0.1744 (b) If a random sample of sixteen 18-year-old men is selected, what is the probability that the mean height x is between 68 and 70 inches? (Round your answer to four decimal places.) a 0.1153 b 0.5187     c 0.5763 d 0.6339 (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 lower because the standard deviation is smaller for the x distribution. b The probability in part (b) is much higher because the mean is smaller for the x distribution.     c The probability in part (b) is much higher because the standard deviation is smaller for the x distribution. d The probability in part (b) is much higher because the standard deviation is larger for the x distribution

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard deviation 5 inches.

(a) What is the probability that an 18-year-old man selected at random is between 68 and 70 inches tall? (Round your answer to four decimal places.)
a 0.0793
b 0.1585    
c 0.0317
d 0.1744


(b) If a random sample of sixteen 18-year-old men is selected, what is the probability that the mean height x is between 68 and 70 inches? (Round your answer to four decimal places.)
a 0.1153
b 0.5187    
c 0.5763
d 0.6339


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