1. Yolanda has a deck of 10 cards numbered 1 through 10. She is playing a game of chance. This game is this: Yolanda chooses one card from the deck at random. She wins an amount of money equal to the value of the card if an even numbered card is drawn. She loses $7 if an odd numbered card is drawn. (If necessary, consult a list of formulas.) (a) Find the expected value of playing the game. dollars (b) What can Yolanda expect in the long run, after playing the game many times? (She replaces the card in the deck each time.)

O Yolanda can expect to gain money. She can expect to win____dollars per draw.

O Yolanda can expect to lose money. She can expect to lose____dollars per draw.

O Yolanda can expect to break even (neither gain nor lose money).

2. 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 0.88) = (b) P (z > 1.14) = (c) P (-0.88 < Z < 2.01) =

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(Z> c) =0.1469 Round your answer to two decimal places.

4. Abdul works for NASA designing planetary rovers. For his current project, he has to design a rover capable of withstanding the harsh climate on the surface of Venus. As part of his design work, Abdul models the daily high surface temperature of Venus using a normal distribution with a mean of 457 C and a standard deviation of 25 C. Use this table or the ALEKS calculator to find the percentage of daily high temperatures less than 442 C or more than 472 C 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 %).

5. According to her doctor, Mrs. Campbell's cholesterol level is higher than only 10% of the females aged 50 and over. The cholesterol levels among females aged 50 and over are approximately normally distributed with a mean of 225 mg/dL and a standard deviation of 20 mg/dL. What is Mrs. Campbell's cholesterol level? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

6. Grand Sun Buffet is a large restaurant chain. After paying for a meal at Grand Sun Buffet, customers are asked to rate the quality of the food as a 1, 2, 3, 4, or 5, where a rating of 1 means "not good" and 5 means "excellent". The customers' ratings have a population mean of =3.63, with a standard deviation of o = 1.65. Suppose that we will take a random sample of n =8 customers' ratings. Let x represent the sample mean of the 8 customers' ratings. 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 - (the mean of the sampling distribution of the sample mean).

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

7. According to records, the amount of precipitation in a certain city on a November day has a mean of 0.10 inches, with a standard deviation of 0.06 inches. What is the probability that the mean daily precipitation will be 0.11 inches or more for a random sample of 40 November days (taken over many years? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

8. A worldwide organization of academics claims that the mean IQ score of its members is 115, with a standard deviation of 15. A randomly selected group of 40 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 116.8. If the organization's claim is correct, what is the probability of having a sample mean of 116.8 or less for a random sample of this size? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

9. Suppose that the scores on a reading ability test are normally distributed with a mean of 65 and a standard deviation of 8. What proportion of individuals score at least 57 points on this test? Round your answer to at least four decimal places.

10. Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, portfolio managers give a questionnaire to new customers to measure their desire to take financial risks. The scores on the questionnaire are approximately normally distributed with a mean of 50.5 and a standard deviation of 15. The customers with scores in the bottom 5% are described as "risk averse." What is the questionnaire score that separates customers who are considered risk averse from those who are not? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.