9 A study of commuting times reports the travel times to wor

9. A study of commuting times reports the travel times to work of a random sample of 50   employed adults in New Your State. The mean of this sample is 31.25 minutes. In various other studies, the commuting times of travel to work have a mean of 35.3 minutes and standard deviation is 14 minutes.

a)Find muse of x bar

b)Find .sigma of x bar

c)Describe the sampling distribution of x bar .   Justify your answer.

d)P(X > 31.25) =

e)P( > 31.25) =  

F)Why are the values so different in d) and e) ?

g)What can one conclude from the probability of the sample mean of 31.25 with n = 50?

Solution

a)Find muse of x bar

mu=35.3

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b)Find .sigma of x bar

s/vn=14/sqrt(50) = 1.979899

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c)Describe the sampling distribution of x bar .   Justify your answer.

Normal distriubtion

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d)P(X > 31.25) = P((X-mean)/s >(31.25-35.3)/14)

=P(Z>-0.29) =0.6141 (from standard normal table)

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e)P( xbar> 31.25) = P((xbar-mean)/(s/vn) >(31.25-35.3)/1.979899)

=P(Z>-2.05) = 0.9798 (from standard normal table)

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F)Why are the values so different in d) and e) ?

part d is calculated only one observation, but part e is calculated by the mean.

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g)What can one conclude from the probability of the sample mean of 31.25 with n = 50?

Since the probability this high, we can conclude that most observations are greater than 31.25