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# Normal Probabilities and t test for Mean

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The amount of time a bank teller spends with each customer is normally distributed with a mean of 3.10 minutes and a standard
deviation of 0.40 minutes. (Use the z table)
If a random sample of 16 customers is selected from the bank, what is the probability that the average time spent per customer will be at least 3 minutes?

There is an 85 percent chance that the sample mean will be below how many minutes?

Doubting Thomas does not believe that the mean is actually 3.10 minutes since he has often waited longer. He decides to conduct a study and generates a random sample of 25 customers. He calculates the waiting time for all 25 customers and finds the average A waiting time to be 4 minutes. Based on this information, what is the best estimate of the population mean assuming 95 percent accuracy. Is the doubting Thomas correct in his assumption?