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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.

(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 .

(d) What is the probability that Y will be less than 38?

(e) What is the probability that Y will be greater than 45?

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