show me how to calculate the cutoff point when given $500 in an account, $125 std deviation, & upper 8%?

Question

Average daily balance is $500 and std dev. is $125, I want to know how to calculate customers with balances in the highest 8%.

Answer 1

mmm cant write the answer down without knowing the total number of obsevations ... meaning the number of customers u used to find the average in first place

Answer 2

Look up a Normal curve table in any intermediate probability textbook.

By definition, z = (b - m)/s; where b is a daily balance, m = $500 is the average of all daily balances, and s = $125 the standard deviation. Then, find b = sz + m by finding the z where A(x>z) = .08; where A is the area under the Normal curve where the balances exceed some critical value (b) of balances.

In the table I have, A(x>1.40) = .08, which means that 8% of your highest balanced accounts are found where z exceeds 1.40. To find b = sz + m = $125 X 1.4 + $500 = $175 + $500 = $675. Thus, you'll have 8% of your customers (more or less) when you select those with a daily balance of $675 or more.