Assignment Problems 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 = 3 and z = 3? 3. What is the area under a standard normal curve between z = 2.16 and z = 1.58? 4. What is the area under a standard normal curve to the right of z = 2.16? 5. What is the area under a standard normal curve between 2 = 1.82 and z = 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 2 lies between a and b is denoted P(a S 2 S b) and this probability is the same as the area under the curve between the z-scores, 21 = a. and 22 = b. 6. Using a standard normal curve, what is P(1.36 3 z S 1.20)? Section 5.2 7. SAT Math Scores. Suppose the population of SAT math scores follows a normal distribution with p = 563 and a = 139. What is P(575 S :1: S 590)? 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