1. Suppose z follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. (a) P(Z > 2.04) = (b) P (Z 0.84) = (c) P(-1.10 < Z < 2.20) =

2. Suppose z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true. P(Z c) =0.7088 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

3. Suppose z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true. P (0.84 Z c)=0.1717 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

4. According to a recent survey, the salaries of entry-level positions at a large company have a mean of $40,756 and a standard deviation of $6500. Assuming that the salaries of these entry-level positions are normally distributed, find the proportion of employees in entry-level positions at E the company who earn less than $42,000. Round your answer to at least four decimal places.

5. CetaceaNow is a conservationist organization that monitors the health of whale and dolphin populations worldwide. As part of their work, they are modelling the lengths of blue whale calves that will be born over the next decade. For their model, CetaceaNow is using a normal distribution with a mean of 276 in and a standard deviation of 20 in. Use this table or the ALEKS calculator to find the percentage of blue whale calves with a length of between 243 in and 265 in according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).

6. Suppose that scores on a particular test are normally distributed with a mean of no and a standard deviation of 19. What is the minimum score needed to be in the top 5% of the scores on the test Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.

7. The state of California has studied a large population of pregnant women applying for maternity leave. The women stated which trimester of their pregnancy 1, 2, or 3 they are in. The mean response was =1.30, with a standard deviation of =0.68. Suppose that we will take a random sample of =n10 of these women's responses. Let x represent the sample mean of the 10 women's responses. Consider the sampling distribution of the sample mean x. Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed.

(a)Find x (the mean of the sampling distribution of the sample mean). =x

(b)Find x (the standard deviation of the sampling distribution of the sample mean).

8. A study of college football games shows that the number of holding penalties assessed has a mean of 2.2 penalties per game and a standard deviation of 1.05 penalties per game. What is the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2.15 penalties per game or more? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

9. The producer of a weight-loss pill advertises that people who use the Espaol lose, after one week, an average (mean) of 18 pounds with a standard deviation of 1.02 pounds. In a recent study, a group of so people who used this pill were interviewed. The study revealed that these people lost a mean of 1.68 pounds after one week. If the producer's claim is correct, what is the probability that the mean E weight loss after one week on this pill for a random sample of so individuals will be 1.68 pounds or more? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

10. Suppose that the heights of adult women in the United States are normally distributed with a mean of 63.5 inches and a standard deviation of 23 inches. Donna is taller than 80% of the population of U.S. women. How tall (in inches) is Donna? Carry your intermediate computations to g at least four decimal places. Round your answer to one decimal place.

11. Suppose that the speeds of cars travelling on California freeways are normally distributed with a mean of 61 miles/hour. The highway patrol's policy is to issue tickets for cars with speeds exceeding 80 miles/hour. The records show hour that exactly 2% of the speeds exceed this limit. Find the standard deviation of the speeds of cars travelling on California freeways. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

12. Bob, a highway safety inspector, is concerned about the potential for accidents caused by boulders that fall down a sandstone cliff beside a main highway. As part of an accident simulator, Bob models the boulders' weights using a normal distribution with a mean of 567 kg and a standard deviation of 150 kg. Use this table or the ALEKS calculator to find the percentage of boulders that weigh between 273 kg and 645 kg according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).