Answer to Question #189854 in Statistics and Probability for enj

Question

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

Answer 1

Given,

Mean of population $\mu=8$

Standard deviation $\sigma = 5.4$

Using

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

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

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

Hence, Probability P(Z>1.25)= 0.1056