Question

The average words per minute a person can type is 50 words per minute

with standard deviation of 25.5 words. If you choose 25 samples, what is the

probability that the average words they can type is more than 39?

Answer 1

Let $\bar{X}=$ the average words they can type: $\bar{X}\sim N(\mu_{\bar{X}}, \sigma_{\bar{X}}^2)$

$\mu_{\bar{X}}=\mu=50, \sigma_{\bar{X}}={\frac {\sigma} {\sqrt{n}}}={\frac {25.5} {\sqrt{25}}}=5.1$

So,

$$P(\bar{X}>39)=1-P(\bar{X}\leq39)$$ $$=1-P(Z\leq\dfrac{39-50}{5.1})=1-P(Z\leq-2.157)=1-0.01550=0.9845$$