Question

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.)

Answer 1

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