Find the following using the unit normal table.

1. p(z < +1.5)

2. p(z > +0.54)

3. p(z < -1.23)

4. p(z > -1.95)

5. p(-.8 < z < +.8) [i.e., what proportion of a normal distribution is located between z = - .8 and z = +.8?]

6. p(-1.2 < z < +1.2)

7. = 45; s = 12; find p(X > 12)

8. = 14; s = 2.8; find p(X < 8.9)

9. Suppose that the weight of male adult Labrador Retrievers follows a normal distribution with a mean of 68 lbs and a standard deviation of 6 lbs.

a. Your neighbor's Labrador Retriever, Petey, weights 78 lbs. Petey weighs more than how many percent of all male Labrador Retrievers?

b. Twenty percent of all male Labrador Retrievers weighs less than your aunt's dog, Tommy. What is the z-score corresponding to Tommy's weight? How much does he weigh?

c. Your best friend's Labrador Retriever, Wally, weighs less than 40% of all male Labrador Retrievers. What is the z-score corresponding to Wally's weight? How much does he weigh?

10. For a normal distribution, what z-score values form the boundaries that separate the middle 80% of the distribution from the rest of the scores?

11. Suppose that the average body mass index (BMI) for women your age in the population is 24 with a standard deviation of 2. Find the proportion in each of the following BMI categories:

a. Obese: BMI over 30

b. Overweight: BMI between 25 and 30

c. Normal: BMI between 20 and 25

12. A shoe manufacturer collected data on men's shoe sizes and found that the distribution of sizes exactly fits the normal curve, with the mean shoe size being 11 and the standard deviation being 1.5.

a. What is the percentage of men who wear size 10-12 shoes?

b. What shoe size corresponds to the highest 10%?

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