Question

a class of 30 of these pupils is used as sample. what is the probability that the class mean is greater than 46 inches?

Answer 1

Given,

Mean $\mu=45$

Standard deviation $\sigma=2$

Probability that the class mean is greater than 46 =$P(X>46)$

$z=\dfrac{x-\mu}{\sigma}=\dfrac{46-45}{2}=\dfrac{1}{2}=0.5$

Therefore the required probability is $P(z>0.5)=P(0<z<\infty)-P(0<z<0.5)$

$=0.5-0.1915=0.3085$