Answer to Question #345496 in Statistics and Probability for James

Question

What is the probability that the mean weekly income of these 50 workers is less than 448 pesos?

Answer 1

To calculate that, we should know the mean and the standard deviation. To find P we use formula:

$P(\=x<448)=P(z<\frac{448-\mu}{\sigma/\sqrt{n}})$

For example, we have $\mu=500, \sigma=160$

Then $P(z<\frac{448-\mu}{\sigma/\sqrt{n}})=P(z<\frac{448-500}{160/\sqrt{50}})=P(z<-2.29)=0.011$

(We found p using z-table).

So to calculate that you should substitute $\mu,\sigma$ for your numbers and find P.