Question

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?

Answer 1

68%

Explanation:

Answer 2

68,3 %

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