61 Children’s attitude toward reading. In the journal Knowledge Quest (January/February 2002), education professors at the University of Southern California investigated children’s attitudes toward reading. One study measured third through sixth graders’ attitudes toward recreational reading on a 140-point scale (where higher scores indicate a more positive attitude). The mean score for this population of children was 106 points, with a standard deviation of 16.4 points.

Consider a random sample of 36 children from this population, and let x represent the mean recreational reading attitude score for the sample.

a. What is mx ?

b. What is sx ?

c. Describe the shape of the sampling distribution of x.

d. Find the z -score for the value x = 100 points .

e. Find P(x 6 100).