Question

The First Chicago Bank is reviewing its service charges and interest-paying policies on checking accounts. The daily balance of a checking account is defined to be the balance in the checking account at 2:00pm.

The bank has found that for all personal checking accounts the mean of all the daily balances is $ 900 and the standard deviation is $175.

In addition, the distribution of personal checking account daily balances can be approximated very well with a normal model.

Answer 1

What is the probability that a randomly selected personal checking account will have a daily balance of less than $750?

To answer this question, we need to calculate the z-score for a daily balance of $750 using the mean and standard deviation provided:

z = (x - μ) / σ = (750 - 900) / 175 = -0.857

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than -0.857:

P(z < -0.857) = 0.1952

Therefore, the probability that a randomly selected personal checking account will have a daily balance of less than $750 is approximately 0.1952 or 19.52%.