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 _______

In the range: 49 - 51

Concept:

The normal distribution is symmetric with respect to the mean position and the standard normal variate is given by the relation.

Let variate be x

$\mathrm{z}=\frac{\mathrm{x}-\mathrm{M}}{\sigma }$

Where z = Normal variate, M = Mean, σ = Standard deviation

ForP(z ≥ 0) = P(z < 0) = 0.5 or 50%

Calculation:

Given:

M = 500

σ = 50

P(x > 500) = ?



Where X follows the normal distribution

We know that standard normal variable

$\mathrm{z}=\frac{\mathrm{x}-\mathrm{M}}{\sigma }$

converting into normalized form

x = 50z + 500

given, x > 500, therefore

50z + 500 > 500 or z > 0

probability, P(z > 0) = 0.5

∴ P(x > 500) = 0.5 or 50%

For x = 500, the standard normal variate is

$\mathrm{z}=\frac{500-500}{50}=0$

∴ P(x > 500) = P(z > 0) = 0.50 or 50%(See figure)