Suppose the average height of all humans is normally distributed with a mean of 72 inches and a variance of 18 inches. a. Determine P(7580)
b. Determine P(x<65)

a) P(75 < x < 80 ) = 0.2088

b) The probability that  average height of all humans less than 65

P( X < 65 ) = 0.0495

Step-by-step explanation:

Step(i):-

Given mean of the Population = 72

Given variance of the Population = 18 inches.

Standard deviation of the Population = √18 = 4.242

Let 'x' be the random variable in Normal distribution

a)

Given X₁ = 75

Given X₂= 80

The probability that  average height of all humans between 75 and 80

                        = | A ( 1.885) - A( 0.70721|

                       = 0.4699 - 0.2611

                      = 0.2088

P(75 < x < 80 ) = 0.2088

b)

Step(ii):-

Given X₁ = 65

The probability that  average height of all humans less than 65

P( X < 65 ) = P( Z < - 1.650 )

                 = 1 - P( Z > 1.650)

                = 1 - ( 0.5 + A (1.650))

              =  0.5 - A( 1.65)

             = 0.5 - 0.4505

             = 0.0495

The probability that  average height of all humans less than 65

P( X < 65 ) = 0.0495

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