Question

A normally distributed population has a mean of 72 and a standard deviation of 14. Determine the probability that a random sample of size 35 has an average greater than 73. Round to four decimal places.

Answer 1

Solution :

Given that ,

mean = = 72

standard deviation = = 14

n = 35

= 72

= / n = 14/ 35 = 2.3664

P( > 2.3664) = 1 - P( <2.3664 )

= 1 - P[( - ) / < (73 - 72) / 2.3664]

= 1 - P(z < 0.42)

Using z table,    

= 1 - 0.6628

= 0.3372