The Webster National Bank is reviewing its service charge and interest-paying
policies on checking accounts. The bank has found that the average daily balance on
personal checking accounts is $550, with a standard deviation of
$150. In addition,
the average daily balances have been found to be normally distributed (Gaussian).

(a) What percentage of personal checking account customers carry average daily
balances in excess of $800?
(b) What percentage of the banks customers carries average daily balances below
of $200?
(c) What percentage of the banks customers carries average daily balances
between $300 and $700?
(d) The bank is considering paying interest to customers carrying average daily
balances in excess of a certain amount. If the bank does not want to pay
interest to more than 5% of its customers, what is the minimum average daily
balance it should be willing to pay interest on?

Solution Summary

Step by step method for computing probability calculation using Z score is given in the answer.

A normal population has an average of 80 and a standard deviation of 14.0.
Calculate the probability of a value between 75.0 and 90.0.
Calculate the probability of a value of 75.0 or less.
Calculate the probability of a value between 55.0 and 70.0.

I need help with some practice problems that were given to us, to help prepare for a quiz next week. Please provide detailed steps as to how you came by your answer (include any notes, calculations, or anything that may be pertinent to the solution).
As always, your help would be greatly appreciated!
Thanks,
E

On a test whose distribution is approximately normal with a mean of 50 and a standard deviation of 10, the results for three students were reported as follows:
Student Opie has a T-score of 60.
Student Paul has a z-score of -1.00.
Student Quincy has a z-

1. Given that z is a standard normal random variable, compute the following probabilities.
a. p (z = 2.0)
b. p (z ≥ 1.4)
c. p (-1.0 < z < 0.5)
d. p (1.0 < z < 1.2)
2. The time needed to drive from city A to city B is normally distributed with a mean of 180 minutes and standard deviation of 20 minutes.
a. Wha

A normal distribution has a mean of u= 40 and o=10. if a vertical line is drawn through the distribution at x= 55, what proportion of the scores on the right side of the line?
A normal distribution has a u= 80 and o= 10. what is the probability of randomly selecting a score greater than 90 from this distribution?
A normal

Based upon statistical studies it has been found that 3.32% of all births in the United States will result in twins being born. If 17,300 births are selected at random what is the probability that:
a) at most 600 of them will result in twins being born?
b) between 525 and 550 of them (inclusive) will result in twins being born

The actual weight of 2-pound sacks of salted peanuts is found to be normally distributed with a mean equal to 2.04 pounds and a standard deviation of 0.25 pounds. Given this information, the probability of a sack weighing more than 2.40 pounds is 0.4251
True or False?

The KW water is provided to approximately 750,000 people, who are served through more than 362,000 accounts. All accounts are metered and billed monthly. the probability that an account has an error in a month is 0.001, and accounts can be assumed to be independent.
a- what is the mean and standard deviation of the number of ac

Suppose we have a population of scores with a mean (mu) of 200 and a standard deviation (sigma) of 10. Assume that the distribution is normal. Provide answers to the following questions:
1. What score would cut off the top 5 percent of scores?
2. What score would cut off the bottom 5 percent of scores?
3. What scor