Question

The ages of commercial aircraft are normally distributed with a mean of 13.5 years and a standard deviation of 7.8

years. What percentage of individual aircraft have ages greater than 15​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 greater than 15

​years?The percentage of individual aircraft that have ages greater than 15 years is _____ ​%

Answer 1

Solution :

Given that ,

mean = = 13.5

standard deviation = = 7.8

P(x > 15) = 1 - P(x < 15)

= 1 - P((x - ) / < (15 - 13.5) / 7.8)

= 1 - P(z < 0.19)

= 1 - 0.5753 Using standard normal table.

= 0.4247

= 42.47%

The percentage of individual aircraft that have ages greater than 15 years is 42.47%

n = 81

= = 13.5 and

= / n = 7.8 / 81 = 0.8667

P( > 15) = 1 - P( < 15)

= 1 - P(( - ) / < (15 - 13.5) / 0.8667)

= 1 - P(z < 1.73)

= 1 - 0.9582 Using standard normal table.

= 0.0418

= 4.18%

The percentage of sample means have ages greater than 15 is 4.18%.