Question

A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of Rs. 500 and a standard deviation of Rs. 50. The percentage of savings account holders, who maintain an average daily balance more than Rs. 500 is ___.

A. 0.90
B. 0.60
C. 0.40
D. 0.50

Answer 1

To find the percentage of savings account holders who maintain an average daily balance more than Rs. 500, we need to calculate the area under the curve of the normal distribution that is greater than Rs. 500. The answer is 50%.

Step-by-step explanation:

To find the percentage of savings account holders who maintain an average daily balance more than Rs. 500, we need to calculate the area under the curve of the normal distribution that is greater than Rs. 500. We can use the z-score formula to convert Rs. 500 into a z-score:

z = (x - mean) / standard deviation

z = (500 - 500) / 50 = 0

The z-score of 0 corresponds to a cumulative probability of 0.5, so 50% of the savings account holders have a balance more than Rs. 500. The percentage of savings account holders who maintain an average daily balance more than Rs. 500 is 50%.

This is because, in a normal distribution, the mean divides the distribution in half, so the percentage of data points above the mean is equal to the percentage below the mean. Since the daily balance is normally distributed with a mean of Rs. 500, exactly half of the account holders will have balances above this mean, which corresponds to answer option D.

Therefore, the answer is 50%.