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Sampling Distribution of the mean

The amount of time a bank teller spends with each customer has a population mean = 3.1 minutes and population standard deviation = 0.4 minute.
a) What is the probability that for a randomly selected customer the service time would exceed 3 minutes?
b) If many samples of 64 were selected, what are mean and standard error of the mean (standard deviation of sample means) expected to be? What is expected to be the shape of the distribution of sample means? Give reasons for all your answers.
c) If a random sample of 64 customers is selected, what is the probability that the sample mean would exceed 3 minutes?

Solution Preview

The solution is in the attached word file:
The amount of time a bank teller spends with each customer has a population mean M x = 3.1 minutes and population standard deviation sx = 0.4 minute.

a) What is the probability that for a randomly selected customer the service time would exceed 3 minutes?

Mean=M = 3.1 minutes
Standard deviation =s= 0.4 minutes
x= 3 minutes
z=(x-M )/s= -0.25 =(3-3.1)/0.4
Cumulative Probability corresponding to z= -0.25 is= 0.4013
Or Probability corresponding to x< 3.00 is Prob(Z)= 0.4013 0r= 40.13%
Therefore probability corresponding to x> 3.00 is ...

Solution Summary

Probability for sample mean is calculated using Central Limit Theorem.

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