Question

In an all boys school, the height of the student body are normally distributed with a mean of 69 inches and a standard deviation of 5 inches. using the empirical rule, what percentage of the boys are between 54 and 84 inches tall?

Answer 1

Answer:

99.7% of the boys are between 54 and 84 inches tall.

Step-by-step explanation:

The heights 54 and 84 inches are 3 standard deviations away from the mean. Thus, 99.7% of the boys are between 54 and 84 inches tall.

Answer 2

The percentage of the boys are between 54 and 84 inches tall is 99.7%

What is percentage?

Percentage a relative value indicating hundredth parts of any quantity.

What is empirical rule?

The empirical rule or  the three-sigma rule , is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations of the mean.

The empirical rule predicts that 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

From question mean(μ) = 69 in. and  standard deviation(σ)= 5 in.

(µ ± σ) = (69 ± 5)

           =64 - 74

           =68%

(µ ± 2σ) =(69 ± 10)

            =59 -79

            =95%

(µ ± 3σ) =(69 ± 15)

             =54 -84

             = 99.7%

Thus the percentage of the boys are between 54 and 84 inches tall is 99.7%

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