Given a normal population whose mean is 485 and whose standard deviation is 29

| August 30, 2017

Question
1. Given a normal population whose mean is 485 and whose standard deviation is 29, find each of the following:

A. The probability that a random sample of 6 has a mean between 487 and 496. Probability =

B. The probability that a random sample of 16 has a mean between 487 and 496. Probability =

C. The probability that a random sample of 29 has a mean between 487 and 496. Probability =

2. Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank’s Visa cardholders reveals that the amount is normally distributed with a mean of 25 dollars and a standard deviation of 7 dollars.

A. What proportion of the bank’s Visa cardholders pay more than 27 dollars in interest? Proportion =

B. What proportion of the bank’s Visa cardholders pay more than 37 dollars in interest? Proportion =

C. What proportion of the bank’s Visa cardholders pay less than 15 dollars in interest? Proportion =

D. What interest payment is exceeded by only 22% of the bank’s Visa cardholders? Interest Payment

3. College students average 8.4 hours of sleep per night with a standard deviation of 35 minutes. If the amount of sleep is normally distributed, what proportion of college students sleep for more than 9.5 hours?

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