Question

Assume that the probability distribution of the net deposit drain of a Depository Institution (DI) has been estimated to have a mean of 3 per cent of total deposits and a standard deviation of 1 per cent. Is this DI increasing or decreasing in size? Explain.

Below is part of the answer. What I want to know is hot do you get the values between 1 and 5 percent? Also the 95%

If the distribution is normal, we can state with 95 per cent confidence that the rate of decrease of deposits will be between 1 per cent and 5 per cent

Answer 1

See the image below. In the normal distribution, 1 standard deviation around the mean covers approx 68 percent of the data and 2 standard deviation around the mean covers the approx 95 percent of the data. and since the mean is 3 and the standard deviation is 1:

3 - 1 < x < 3 + 1 will cover the 68 percent of the data.

3 - 2 < x < 3 + 2 will cover the 95 percent of the data.

3 - 3 < x < 3 + 3 will cover 99.7 percent of the data.

Since 95 percent confidence interval is the most commonly used in statistics, they have given answer in the term of 95 percent confidence interval. Otherwise, you can also write the answer as

If the distribution is normal, we can state with 68 percent confidence that the rate of decrease of deposits will be between 2 percent and 4 percent

or

If the distribution is normal, we can state with 99.7 percent confidence that the rate of decrease of deposits will be between 0 percent and 6 percent

All the answers will be correct

Remember this percentage as they are very commonly used in statistics.

Hope it helps !