Answer to Question #197782 in Statistics and Probability for Janrey

Question

As a Senior High School Student how much time do you spent in studying

and answering the activities in your modules? Do you

spend 25 hours in a week er

more than that? Suppose that the average number of hours spent by senior high

tool students in your school for their modular classes in a week is 25 hours with

4 standard deviation of 4 hours. Assuming that the study is true and the data is

Normally distributed. What is the probability that a random sample of 12 senior

high school students spends more than 24 hours?

Answer 1

Let $X=$ the average number of hours spent by students: $X\sim N(\mu, \sigma^2/n).$

Given $\mu=25\ h, \sigma=4\ h, n=12.$

$$P(X>24)=1-P(X\leq 24)$$

$$=1-P(Z\leq \dfrac{24-25}{4/\sqrt{12}})\approx1-P(Z\leq-0.866025)$$

$$\approx0.806762$$

The probability that a random sample of 12 senior high school students spends more than 24 hours is $0.806762.$