Sections 2.4 & 5.1

1. Understanding the normal curve. In the standard normal distribution, the cumulative area for a standard score of -3.49 is close to what value?

2. Empirical rule. Using the empirical rule, what percentage of the area under the standard normal curve would you expect between the z=3z=3 and z=3z=3?

3. What is the area under a standard normal curve between z=2.16z=2.16 and z=1.58z=1.58?

4. What is the area under a standard normal curve to the right of z=2.16z=2.16?

5. What is the area under a standard normal curve between z=1.82z=1.82 and z=1.14z=1.14

Problem 6. Answer the question using the following information. The normal distribution is a type of probability density function. Areas found under this curve are equivalent to probabilities. For example, the probability that z lies between a and b is denoted P(azb)P(azb) and this probability is the same as the area under the curve between the z-scores, z1=az1=a and z2=bz2=b.

6. Using a standard normal curve, what is P(1.36z1.20)P(1.36z1.20)?

Section 5.2

7. SAT Math Scores. Suppose the population of SAT math scores follows a normal distribution with =563=563 and =139=139. What is P(575x590)P(575x590)?

Problems 8-10. The weights of a group of young people are normally distributed, with a mean of 160 pounds and a standard deviation of 8 pounds. A young person is randomly selected.

8. Find the probability that the young person's weight is less than 135 pounds.

9. Find the probability that the young person's weight is between 135 and 170 pounds.

10. Find the probability that the young person's weight is more than 170 pounds.

Section 5.3

Problems 11-12. Use the Standard Normal Distribution Table to find the z-score that corresponds to the given cumulative area. If the area is not in the table use the entry closest to the area, unless the area is exactly halfway between two entries. In that case, use the z-score halfway between the corresponding z-scores.

11. Area=0.2981Area=0.2981

12. Area=0.9844Area=0.9844

13. A normal distribution has =185=185 and =7.4=7.4. Find the xx-value that has 28.4% of the standard normal distribution's area to its left.

Section 5.4

Problems 14-15. A population with n=275n=275 has a mean =624=624 and a standard deviation =36=36.

14. Find xx.

15. Find xx.

16.True or false? As the size of a sample decreases, the standard deviation of the distribution of sample means decreases.

Problems 17-18. A sample with n=750n=750 is taken from a population that has a mean, =125=125 and the standard deviation, =25=25.

17. What is P(x<123)P(x<123)?

18. Would it be considered unusual if x<123x<123? (Note: See FAQ 4.4.)

19. Nurse Salaries. The population mean annual salary for registered nurses is $58,642. A random sample of 30 registered nurses is selected from this population. What is the probability that the mean annual salary of the sample is greater than $59,500? Assume =$2200=$2200.