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

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