Answer to Question #336163 in Statistics and Probability for Shoula

Question

It is reported that the average number of hours of sleep of a college student during regular school days is 6 hours a day .If 28 college students were randomly selected find the probability that the mean number of hours they sleep during regular school days is longer than 6.8 hours .Assume that the variable is normally distributed with standard deviation of 1.2 hours

Answer 1

$$P(\bar{X}>6.8)=1-P(Z\le\dfrac{6.8-6}{1.2/\sqrt{28}})$$

$$\approx0.00020962$$