Question #189854

a population size N = 150 has μ = 8 and standard deviation of 5.4. What is the probability that a random size n=20 will have a mean of 9.5 above


1
Expert's answer
2021-05-07T14:18:40-0400

Given,

Mean of population μ=8\mu=8

Standard deviation σ=5.4\sigma = 5.4

Using

P(Xˉ>9.5)=XˉμσnP(\bar X >9.5)= \dfrac{\bar X-\mu}{\frac{\sigma}{\sqrt n}}


P(Xˉ>9.5)=9.585.420=1.51.20=1.25P( \bar X>9.5)= \dfrac{9.5-8}{\frac{5.4}{\sqrt{20}}}=\dfrac{1.5}{1.20}=1.25


So, P(Z>1.25)=0.1056P(Z>1.25)=0.1056





Hence, Probability P(Z>1.25)= 0.1056


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