Question

A population of adult males had their heights measured. The heights were normally distributed. Approximately

what percentage of the heights, rounded to the nearest whole number, are within one standard deviation of the
mean?

Answer 1

The percentage of the heights that lie within one standard deviation of the mean height is 68%.

Explanation:

Here it is given that the heights of adult males of a population are distributed normally.

The Empirical Rule states that in a normal distribution with mean µ and standard deviation σ, nearly all the data will fall within 3 standard deviations of the mean. The empirical rule can be divided into three parts:

• 68% data falls within 1 standard deviation of the mean.

That is P (µ - σ ≤ X ≤ µ + σ) = 0.68.

• 95% data falls within 2 standard deviations of the mean.

That is P (µ - 2σ ≤ X ≤ µ + 2σ) = 0.95.

• 99.7% data falls within 3 standard deviations of the mean.

That is P (µ - 3σ ≤ X ≤ µ + 3σ) = 0.997.

So, the percentage of the heights that lie within one standard deviation of the mean height is 68%.