In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 5 inches. Using the empirical rule, what percentage of the boys are between 65 and 75 inches tall?

68,3 %

Step-by-step explanation:

Empirical rule establishes:

In a normal distribution with mean μ and standard deviation σ we have a relation between values of the distribution and intervals describes as follows:

(μ ± σ) contains 68.3 % of all values of the distribution

(μ ± 2σ) contains 95,4 % and

(μ ± 3σ) contains 99.7 %

In our particular case we have that

(μ ± σ) ⇒ (70 ± 5) ⇒ (65, 75)

(μ ± 2σ) ⇒ (70 ± 10) ⇒ (60, 80) and

(μ ± 3σ) ⇒ (70 ± 15) ⇒ (55, 85

As we can clearly see 68,3 % of values fall between values going from 65 up to 75 inches