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.

Individual scores of a placement examination are normally distributed with a mean of 84.2 and a standard deviation of 12.8.
If the score of an individual is randomly selected, find the probability that the score will be less than 90.0.
If a random sample of size n = 20 is selected, find the probability that the sample mean

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.

The department of Weston Materials, Inc. manufacturer of demountable carports, indicates that two workers take an average of 32 hours with a standard deviation of two hours to build a garage. Suppose that the times are joining a normal distribution. (Closer to 2 decimal places)
1. Determine the value of z for 29 hours.
2 De

A normal distributed population has a mean of 250 pounds and a standard deviation of 10 pounds. Given n = 20, what is the probability that this sample will have a mean value between 245 and 255 pounds?

In a particular region of Cape Cod, it is known that lobstermen trap on average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?
Round your answer to four decimal places.

34. Information from the American Institute of Insurance indicates the mean amount of life
insurance per household in the United States is $110,000. This distribution follows the
normal distribution with a standard deviation of $40,000.
a. If we select a random sample of 50 households, what is the standard error of the mean?

Given a standard normal distribution, determine the following: Show Table values used.
Given a standard normal distribution, determine the following: Show Table values used.
a) P( Z < 1.32) =?
b) P(Z>1.32) = ?
c) P(Z<-1.32) =?
d) P(-.30

Data from a National Health Survey show that men's average weight is normally distributed with a mean of 170 pounds and a standard deviation of 30 pounds.
A. If A man is chosen at random, what is the probability that his weight is greater than 180 pounds?
B. If 100 men are randomly selected, what is the probability that TH

A test has a mean of 30, a standard deviation of 6, and scores that are normally distributed. Of the 50 people who took the test, about how many people would be expected to score between 24 and 36?
A. 25 people
B. 34 people
C. 47 people
D. There is not enough information to tell