The mean duration of the flights from Chicago to Dallas is 135 minutes. Assume t

Question

The mean duration of the flights from Chicago to Dallas is 135 minutes. Assume the flight time follows a normal distribution with a standard deviation of 8 minutes. Suppose we select a sample of 16 flights from Chicago to Dallas. a. What can we say about the shape of the distribution of the sample mean? b. What is the standard error of the mean? c. What percent of the sample means will be greater than 140 minutes? d. What percent of the sample means will be greater than 128 minutes? e. What percent of the sample means will be greater than 128 but less than 140 minutes?

Explanation / Answer

a.
The shape of the distribution is approximately normal

b.
Standard error of the mean = (sd/Sqrt(n) = 8/ Sqrt ( 16 ) = 2

c.
P(X > 140) = (140-135)/8/ Sqrt ( 16 )
= 5/2= 2.5
= P ( Z >2.5) From Standard Normal Table
= 0.0062                  

0.62% are above 140

d.
P(X > 128) = (128-135)/8/ Sqrt ( 16 )
= -7/2= -3.5
= P ( Z >-3.5) From Standard Normal Table
= 0.9998                  

99.98% are above 128

e.
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 128) = (128-135)/8/ Sqrt ( 16 )
= -7/2
= -3.5
= P ( Z <-3.5) From Standard Normal Table
= 0.00023
P(X < 140) = (140-135)/8/ Sqrt ( 16 )
= 5/2 = 2.5
= P ( Z <2.5) From Standard Normal Table
= 0.99379
P(128 < X < 140) = 0.99379-0.00023 = 0.9936      

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