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.
(Give answers to 4 decimal places.)
a) What is ?x?
b) What is ?x?
c) What sample mean would be the cutoff for the bottom 10% of sample means. (You are being asked for the 10th percentile of sample means.)
d) Find P(x < 100).