Answer to Question #254873 in Statistics and Probability for Clark

Question

The average words per minute a person can type is 50 words per minute with standard deviation of 2.5 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: $\bar{X}\sim N(\mu_{\bar{X}}, \sigma_{\bar{X}}^2)$

$\mu_{\bar{X}}=\mu=50, \sigma_{\bar{X}}=\sigma/\sqrt{n}=2.5/\sqrt{25}$

$$P(\bar{X}>39)=1-P(\bar{X}\leq39)$$

$$=1-P(Z\leq\dfrac{39-50}{2.5/\sqrt{25}})=1-P(Z\leq-22)\approx1$$