Question

Height of 18-year-old male are normally distributed with a mean of 68 inches and a standard deviation of 3 inches. If a random sample of nine 18-year-old males are selected, what is the probability that the mean height x of the random sample of 9 is greater than 69 inches?

Answer 1

Solution :

Given that,

mean = = 68

standard deviation = = 3

n=9

= =68

= / n = 3/ 9 = 1

P( >69 ) = 1 - P( < 69)

= 1 - P[( - ) / < (69 - 68) /1 ]

= 1 - P(z < 1)

Using z table

= 1 - 0.8413

= 0.1587

probability= 0.1587