Question

The heights of adult women are normally distributed with a mean of 62.5 inches and a standard deviation of 2.5 inches. Determine between what two heights 99.7% of adult women will fall.​

Answer 1

( 55 , 70) interval in which we find 99,7 % of women heights

Explanation:

In Nomal Distribution, N ( 0,1) we know the intervals:

(μ₀ ± σ) contains 68,3 % of all values of population

(μ₀ ± 2 σ) contains 95,4 % of all values of population

(μ₀ ± 3 σ) contains 99,7 % of all values of population

In our case, as μ = 62,5 and standard deviation σ = 2,5 we have that these intervals becomes:

( 62,5 - 2,5 , 62,5 + 2,5 ) ⇒ ( 60 , 65 )

( 62,5 - 2*2,5 , 62,5 + 2* 2,5 ) ⇒ ( 57,5 , 67,5 )

And

( 62,5 - 3*2,5 , 62,5 + 3* 2,5 ) ⇒ ( 55 , 70)

This interval contains 99,7 % of all values