Question

the ages of commercial aircraft are normally distributed with a mean of 13.0 years and a standard deviation of 7.7159 years. what percentage of individual aircraft have ages between 10 years and 16 years? assume that a random sample of 49 aircraft is selected and the mean age of the sample is computed. what percentage of sample means have ages between 10 years and 16 years?

Answer 1

Solution :

Given that,

mean = = 13.0

standard deviation = = 7.7159

n = 49

= 13.0

= / n = 7.7159 / 49 = 1.1023

P( 10 < < 16)  

= P[( 10 - 13.0 ) / 1.1023 < ( - ) / < ( 16 - 13.0) / 1.1023)]

= P( -2.72 < Z < 2.72 )

= P(Z < 2.72 ) - P(Z < -2.72 )

Using z table,  

= 0.9967 - 0.0033

= 0.9934

= 99.34%

Answer : P( 10 < < 16) = 99.34%