Respuesta :
Answer:
The probability that the average of the 100 residents selected is less than 68.5 years is
P( x⁻< 68.5) = 0.1949
Step-by-step explanation:
Step(i):-
Given mean of the Population = 69
Given standard deviation of the Population = 5.8 years
Let x⁻ be the average random variable in normal distribution
Given x⁻ = 68.5
By using
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{68.5-69 }{\frac{5.8}{\sqrt{100} } }[/tex]
Z = -0.862
Step(ii):-
The probability that the average of the 100 residents selected is less than 68.5 years is
P( x⁻< 68.5) = P( z <-0.862)
= 1- P( Z >- 0.862)
= 1 - ( 0.5 + A(-0.862)
= 0.5 - A( 0.862) ( A( -Z) = A(Z))
= 0.5 - 0.3051
= 0.1949
Conclusion:-
The percentage of the probability that the average of the 100 residents selected is less than 68.5 years = 19 %
