Question

The number of hours per week that high school seniors spend on computers is normally distributed with a mean of 5 hours and a standard deviation of 2 hours. 70 students are chose at random, let x̅ represent the mean number of hours spent on a computer for this group. Find the probability that x̅ is between 5.1 and 5.7.

Answer 1

Let X is a random variable denoting the number of hours per week that high school seniors spend on computers.

Given, X is normally distributed with mean of 5 hours and a standard deviation of 2 hours , i.e. X ~ N(5 , 22)

Sample size, n = 70

By cental limit theorem the sampling distribution of the mean() is normally distributed with mean μX and standard deviation σX / √n .

In this context,

The probability that x̅ is between 5.1 and 5.7

                                       

                                       

                                       

                                       

                                      

where,

P ( Z<2.9283 ) is computed form normal table as follow:

P ( Z<0.4183 ) is computed form normal table as follow: