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ACME Fruit Distributing knows that for the last four years, the mean (or average) time it takes a particular truck to make its rounds has been 6.32 hours with standard deviation 0.41 hours. (a) Suppose you plan to observe this truck 40 times. What is the approximate distribution of the random sample mean time? Also specify its parameters. (b) What is the approximate probability that this random sample mean (with n=40) will be more than 6.7 hours? (c) The truck route driver recently retired and Kyle took his place. Would observing Kyle’s time on one particular day to be 6.1 hours cause you to think he is certainly a better driver than the previous one? Explain.(d) Would observing Kyle’s mean (average) time on 40 consecutive days to be 6.1 hours cause you to think he is certainly a better driver than the previous one? Explain.

Question

ACME Fruit Distributing knows that for the last four years, the mean (or
average) time it takes a particular truck to make its rounds has been 6.32 hours
with standard deviation 0.41 hours.
(a) Suppose you plan to observe this truck 40 times. What is the
approximate distribution of the random sample mean time? Also
specify its parameters.
(b) What is the approximate probability that this random sample mean
(with n=40) will be more than 6.7 hours?
(c) The truck route driver recently retired and Kyle took his place. Would
observing Kyle’s time on one particular day to be 6.1 hours cause you
to think he is certainly a better driver than the previous one? Explain.

(d) Would observing Kyle’s mean (average) time on 40 consecutive days
to be 6.1 hours cause you to think he is certainly a better driver than the
previous one? Explain.

check_circleAnswer
Step 1

We are given that ACME Fruit Distributing knows that for the last four years, the mean (or average) time it takes a particular truck to make its rounds has been 6.32 hours with standard deviation 0.41 hours. 

(a) Suppose you plan to observe this truck 40 times. What is the approximate distribution of the random sample mean time? Also specify its parameters.

Answer: Since the sample size is large enough to consider its distribution to be normal. Therefore, according to central limit theorem the distribution of sample mean is approximately normal with mean and standard deviation given:

 

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Step 2

(b) What is the approximate probability that this random sample mean (with n=40) will be more than 6.7 hours?

Answer: 

 

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Step 3

(c) The truck route driver recently retired and Kyle took his place. Would observing Kyle’s time on one particular day to be 6.1 hours cause you to think he is certainly a better driver than the previous one? Explain.

Answer:  We are given mean time for a truck driver is 6.32 and standard deviation is 0.41.

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