The principal of a charter school in Tampa believes that the IQs of its students are above the national average of 100. From the past experience, IQ is normally distributed with a standard deviation of 10. A random sample of 20 students is selected from this school and their IQs are observed. The following are the observed values.
95 91 110 93 133 119 113 107 110 89
113 100 100 124 116 113 110 106 115 113
(a) Test for the normality of the data
(b) Do the IQs of students at the school run above the national average at α = 0.01?