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
(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?
Step by step method for computing probability calculation using Z score is given in the answer.
Statistics: Z-score, sample standard deviation, standardized score
1. For a population with µ=50 and σ=10,
A. What is the z-score for X=55, X=60, X=75, X=45, X=30 and X=35?
B. Find the X value that corresponds to each of the following z-scores, z=1.00, z=0.80, z=1.50, z= -0.50, z= -0.30 and z= -1.50.
2. Find the z-score corresponding to a score of X=60 for each of the following distributions.
A. µ=50 and σ=10
B. µ=50 and σ=5
C. µ=70 and σ=20
D. µ=70 and σ=5
3. For a sample with a mean of M=85, a score of X=90 corresponds to z=0.50. What is the sample standard deviation?
4. In a population of exam scores, a score of X=88 corresponds to z=+2.00 and a score of X=79 corresponds to z= -1.00. What is the means for the population? What is the standard deviation for the population?
5. A distribution with a means of µ=38 and a standard deviation of σ=20 is being transformed into a standardized distribution with µ=50 and σ=10. Find the new, standardized score for each of the following values from the original population.
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