Question

Suppose the heights of males on campus are normally distributed with a mean of 69 inches and standard deviation of 2.5 inches. You plan to choose a random sample of 14 males from the student directory.

a. What is the probability the mean height for your sample will be greater than 70.5 inches?

b. The sample size you used was fairly small. Does this affect the validity of the probability you calculated in (a)?

Answer 1

Solution :

Given that ,

mean = = 69

standard deviation = = 2.5

n = 14

= 69

= / n = 2.5 / 14 = 0.6682

P( >70.5 ) = 1 - P( <70.5 )

= 1 - P[( - ) / < (70.5 -69) / 0.6682]

= 1 - P(z <2.24 )

Using z table

= 1 - 0.9875

= 0.0125

probability= 0.0125

(B)yes any sample size small ,large valid for the probability