Answer to Question #323460 in Statistics and Probability for Ahlsy

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 or more than that? Suppose that the average number of hours spent by senior high school students in your school for their modular classes in a week is 25 hours with  a 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

$P\left( \bar{x}>24 \right) =P\left( \sqrt{n}\frac{\bar{x}-\mu}{\sigma}>\sqrt{n}\frac{24-\mu}{\sigma} \right) =P\left( Z>\sqrt{12}\frac{24-25}{4} \right) =1-\varPhi \left( -0.866025 \right) =1-0.1932=0.8068$