GATE ME 2014 Set 4 — Question 14
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Engineering Mathematics → Statistics & Distributions → Normal Distribution
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Question
A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of Rs. and a standard deviation of Rs. . The percentage of savings account holders, who maintain an average daily balance more than Rs. is _______
Correct answer
49 to 51
Solution
Given that the daily balance follows a normal distribution with mean and standard deviation .A normal distribution is symmetric about its mean . This means that the area under the probability density function curve to the right of the mean is exactly , and the area to the left is also .Mathematically, for a normal distribution :In this problem, we are asked for the percentage of account holders who maintain a balance more than the mean (Rs. ):To express this as a percentage:Thus, of the savings account holders maintain an average daily balance more than Rs. .
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