Question

A sample of size 39 will be drawn from a population with mean 23 and standard deviation 10. Find the probability that  will be greater than 25.

Answer 1

Let $X$ be a random variable of a sample of size 39 from a population which is normally distributed with mean $23$ and standard deviation $10.$

Then $\mu =23$ and $\sigma =10$

Let $Z=\frac {X-\mu}{\sigma}.$ Then $Z=\frac{X-23}{10}$.

We have to find $P(X>25).$

$\therefore P(X>25)=P(Z>\frac{25-23}{10})$

$=P(Z>0.2)$

$=0.5-P(0\leq Z\leq0.2)$

$=(0.5-0.0792)$ $=0.42$

So the required probability is $=0.42$