# What is the probability that x is more than 1 standard deviation from its mean value?

Solution:

The probability that x is more than one standard deviation is 0.3143.

From the normal standard table the area within one standard deviation is 0.3143. Hence the area beyond one standard deviation is 0.5 - 0.3413 = 0.1587 from the centre of the normal distribution. Similarly, the relevant area beyond one standard deviation on the left hand side of the centre of the normal distribution curve is also 0.1826.

Hence the probability of value of x being beyond one standard deviation is 0.1587 x 2 = 0.3174

The probability is depicted in the diagram by the shaded area. The areas add up to 0.3174 and hence the probability of mean of x being beyond one standard deviation will be 0.3174

## What is the probability that x is more than 1 standard deviation from its mean value?

**Summary:**

The probability of the mean of x being beyond one σ (z =1) is given by the areas under the normal distribution curve beyond 1𝜎 from the mean value of x. The probability of this happening is 0.3174 of 31.74%.