Respuesta :
Answer:
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
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{75-72}{4.242} = 0.70721[/tex]
Given X₂= 80
[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{80-72}{4.242} = 1.885[/tex]
The probability that average height of all humans between 75 and 80
[tex]P(75 < X < 80 ) = P(0.70721 < Z < 1.885)[/tex]
= | A ( 1.885) - A( 0.70721|
= 0.4699 - 0.2611
= 0.2088
P(75 < x < 80 ) = 0.2088
b)
Step(ii):-
Given X₁ = 65
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{65-72}{4.242} = -1.650[/tex]
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
