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 0.0793b 0.1585 c 0.0317d 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 0.1153b 0.5187 c 0.5763d 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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Answered: Suppose the heights of 18-year-old men…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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

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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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