Respuesta :
Answer:
D) 0.16
The approximate probability that a randomly selected person in this sample is shorter than 66.8 inches
P(X< 66.8) = 0.16
Step-by-step explanation:
Given data sample of heights of US women is normally distributed with a mean height of 69.4 inches and a standard deviation of 2.6 inches.
mean of the Population μ = 69.4 inches
Standard deviation of the Population σ = 2.6 inches
Let 'X' be the Random variable in Normal distribution
[tex]Z = \frac{x-mean}{S.D}[/tex]
Here x = 66.8 , μ = 69.4 inches and σ = 2.6 inches
[tex]Z = \frac{66.8-69.4}{2.6}[/tex]
Z = -1 < 0
The probability that a randomly selected person in this sample is shorter than 66.8 inches.
P(X< 66.8) = P( Z < -1)
= 1 - p(z > 1) ( by symmetry of normal curve)
= 1 - [ 0.5 + A(1)] [ A(-1) = A(1)]
= 0.5 - A(1)
= 0.5 -0.3413 (from normal table )
= 0.1587
P(X< 66.8) = 0.16
The approximate probability that a randomly selected person in this sample is shorter than 66.8 inches
P(X< 66.8) = 0.16
