Question

The ages of commercial aircraft are normally distributed with a mean of 13.5 years and a standard deviation of 8.3693 years. What percentage of individual aircraft have ages between 9 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 9 years and 16 ​years?

The percentage of individual aircraft that have ages between 9 years and 16 years is ​32.

The percentage of sample means that have ages between 9 years and 16 years is nothing ​%. ​(Round to the nearest tenth as​ needed.)

Answer 1

 

Mean = 13.5, S.D = 8.3693

a) The percentage of individual aircraft have ages between 9 years and 16 years is 32.2%.

x₁ = 9.0

x₂ = 16.0

By applying normal distribution:-

z₁ = - 0.538

z₂ = 0.299

P( - 0.538 < z < 0.299) = P(z > - 0.538) - P(z > 0.299)

P( - 0.538 < z < 0.299) = 0.7047 - 0.3825

P( - 0.538 < z < 0.299) = 0.3222

b) The percentage of sample means have ages between 9 years and 16 ​years is 98.2%.

x₁ =

x₂ =

By applying normal distribution:-

z₁ = - 3.764

z₂ = 2.091

P( - 3.764 < z < 2.091) = P(z > -3.764) - P(z > 2.091)

P( - 3.764 < z < 2.091) = 0.9999 - 0.0183

P( - 3.764 < z < 2.091) = 0.9816