Question

The first chigo 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 2:00 pm. The bank has found that for all personal checking accounts the mean of all the daily balances is $850 and the standard deviation is $200. In addition, the distribution of personal checking account daily balances can be approximated very well with a normal model.

What percentage of the bank's customers carry daily balances between $700 and $1,000 ?
__________ % (Use 2 decimal places in your answer. Note that the answer is requested as a percent, that is, a value between 0 and 100 ).

Answer 1

To find the percentage of customers with daily balances between $700 and $1,000, we calculate the z-scores for these balances using the provided mean and standard deviation. Using the standard normal distribution table or a calculator, we find that approximately 64.5% of the bank's customers fall within this range.

Step-by-step explanation:

To find the percentage of the bank's customers who carry daily balances between $700 and $1,000, we need to calculate the z-scores for these balances using the mean and standard deviation provided. The z-score formula is z = (x - μ) / σ where x is the balance, μ is the mean, and σ is the standard deviation.

For $700:

z = (700 - 850) / 200 = -0.75

For $1000:

z = (1000 - 850) / 200 = 0.75

We can then use a standard normal distribution table or a calculator to find the percentage of values between these z-scores. The area between -0.75 and 0.75 is approximately 0.645. Multiplying by 100 gives us 64.5%, so approximately 64.5% of the bank's customers carry daily balances between $700 and $1,000.