Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 69 inches and standard
deviation 6 inches.
(b) If a random sample of twenty-seven 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.)
Solution :
Given that,
mean = = 69
standard deviation = = 6
n = 27
_{} = = 69
_{} = / n = 6 / 27 = 1.15
P(68 < < 70)
= P[(68 - 69) / 1.15 < ( - _{}) / _{} < (70 - 69) / 1.15)]
= P(-0.87 < Z < 0.87)
= P(Z < 0.87) - P(Z < -0.87)
Using z table,
= 0.8078 - 0.1922
= 0.6156
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