In: Math
The ages of commercial aircraft are normally distributed with a mean of 13.5 years and a standard deviation of 8.2933 years. What percentage of individual aircraft have ages between 10 years and 16 years? Assume that a random sample of 81 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?
Solution :
Given that,
mean =
= 13.5
standard deviation =
= 8.2933
n=81
= 13.5
=
/
n = 8.2933 /
81=0.92
= P(10<
< 16) = P[(10-13.5) /8.2933 < (
-
) /
< (16-13.5) / 8.2933)]
= P( -0.42< Z <0.30 )
= P(Z <0.30 ) - P(Z < -0.42)
Using z table,
= 0.6179-0.3372
= 0.2807
=28.07%