7.1 A jar contains 10 black marbles and 40 white marbles. a. If you randomly select a marble from the jar, what is the probability that you will get a white marble? b. If you are selecting a random sample of n = 3 marbles, and the first 2 marbles are both white, what is the probability that the third marble will be black? 7.2 For each of the following z-scores, sketch a normal distribution and draw a vertical line at the location of the z-score. Then, determine whether the body is to the right or the left of the z-score and find the proportion of the distribution located in the body. a. z = -0.33 b. z = 0.75 c. z = 1.96 d. z = -0.67 7.3 The distribution of scores on the SAT test is approximately normal with = 500 and = 100. a. What proportion of the population have SAT scores above 575? b. What proportion of the population have SAT scores below 520? c. What is the minimum SAT score needed to be in the highest 30% ofthe population? d. What SAT score separates the top 65% from the rest of the distribution? 8.1 For each of the following, assume that the sample was selected from a population with = 72 and = 10. a. What do you expect the value of M to be in a perfect world with no sampling error, if you have a sample of n = 4 scores? b. What is the standard error of M for a sample of n = 4 scores? c. What do you expect the value of M to be in a perfect world with no sampling error, if you have a sample of n = 25 scores? d. What is the standard error of M for a sample of n = 25 scores? 8.2 A population has a mean of = 65 and a standard deviation of = 15. a. If you select a random sample of n = 4 scores from this population, how much error would you expect between the sample mean and the population mean? b. If you select a random sample of n = 25 scores from this population, how much error would you expect between the sample mean and the population mean? c. How much error would you expect for a sample of n = 100 scores? 8.3 Welsch, Davis, Burke, and Williams (2002) conducted a study to evaluate the effectiveness of a carbohydrate-electrolyte drink on sports performance and endurance. Experienced athletes were given either a carbohydrate-electrolyte drink or a placebo while they were tested on a series of high-intensity exercises. One measure was how much time it took for the athletes to run to fatigue. Data similar to the results obtained in the study are shown in the following table: Time to run to fatigue (in minutes) Group, Mean , SE (standard error) Placebo 21.7 2.2 Carbohydrate-electrolyte 28.6 2.7 a. Construct a bar graph that incorporates all of the information in the table. b. Looking at your graph, do you think that the carbohydrate-electrolyte drink helps performance