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The ages of commercial aircraft are normally distributed with a mean of 13.5 years and a...

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?

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Expert Solution

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%

milcah answered 1 year ago
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