1. A random sample of 35 items is drawn from a population with mean 75 and standard deviation 15.
(a) What is the distribution of Y?
(b) Sketch the density function of Y, labeling the mean and standard deviation.
(c) Give a range of values that is almost certain to contain Y.
(d) What is the probability that Y will be greater than 80?
(e) What is the probability that Y will be less than 72?
(f) What is the probability that Y will be greater than 68?
2. A random sample of 47 items is drawn from a population with mean 40 and standard deviation 10.
(a) Sketch the density function of Y, labeling the mean and standard devi- ation.
(b) Give a range of values that is almost certain to contain Y .
(c) What is the probability that Y will be greater than 50?
(d) What is the probability that Y will be less than 38?
(e) What is the probability that Y will be greater than 45?