Respuesta :
Answer:
The probability that the mean is less than 110
P(x⁻<110) =0.5
Step-by-step explanation:
Explanation:-
Given the standard deviation of the Population' σ' = 1250
Given sample size 'n' = 350
The standard error of the mean determined by
[tex]S.E = \frac{S.D}{\sqrt{n} }[/tex]
Standard error = [tex]\frac{1250}{\sqrt{350} } = 66.8153[/tex]
by using normal distribution [tex]z = \frac{x -mean}{S.E}[/tex]
[tex]z = \frac{x^{-} -110}{66.8}[/tex]
cross multiplication 66.8z = x⁻-110
x⁻ = 66.81Z+110
P(x⁻<110)=P(66.81Z+110<110)
= P(66.81Z < 110-110)
= P(66.81Z<0)
= P(Z<0)
= 0.5- A(z₁)
= 0.5 - A(0) (here z₁=0)
= 0.5 -0.00
=0.5
Conclusion:-
The probability that the mean is less than 110
P(x⁻<110) =0.5
