Question 1 Stanford—Binet IQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 16. 3 Sketch the distribution of Stanford-Binet IQ Test scores. b Write the equation that gives the z score corresponding to a Stanford-Binet IQ Test score. Sketch the distribution of such z scores. C Find the probability that a randomly selected person has an IQ test score (1) Over 140. (2) Under 88. (3) Between 72 and 128. (4) Within 1.5 standard deviations of the mean. d Suppose you take the Stanford—Binet IQ Test and receive a score of 136. What percentage of people would receive a score higher than yours? Question 2 When a store uses electronic article surveillance (EAS) to combat shoplifting, it places a small sensor on each item of merchandise. When an item is legitimately purchased, the sales clerk is supposed to remove the sensor to prevent an alarm from sounding as the customer exits the store. In an actual survey of 250 consumers, 40 said that if they were to set off an EAS alarm because store personnel (mistakenly) failed to deactivate merchandise. they would never shop at that store again. A company marketing the alarm system claimed that no more than 5 percent of all consumers would say that they would never shop at that store again if they were subjected to a false alarm. a Assuming that the company’s claim is valid, use the normal approximation to the binomial to calculate the probability that at least 40 of the 250 randomly selected consumers would say that they would never shop at that store again if they were subjected to a false alarm. b Do you believe the companyls claim based on your answer to part rt‘? Explain. Question 3 Suppose that an airline quotes a flight time of 2 hours, 10 minutes between two cities. Furthermore, suppose that historical flight records indicate that the actual flight time between the two cities. is uniformly distributed between 2 hours and 2 hours, 20 minutes. Letting the time unit be one minute, 3 Write the formula for the probability curve of X. b Graph the probability curve of .\'. C Find P(125 5 x £3 135). d Find the probability that a randomly selected flight between the two cities will be at least five minutes late. Question 4 An industry representative claims that 50 percent of all satellite dish owners subscribe to at least one premium movie channel. In an attempt to justify this claim. the representative will poll a randomly selected sample of dish owners. a Suppose that the representative’s claim is true. and suppose that a sample of four dish owners is randomly selected. Assuming independence. use an appropriate formula to compute (1) The probability that none of the dish owners in the sample subscribes to at least one premium movie channel. (2) The probability that more than two dish owners in the sample subscribe to at least one premium movie channel b Suppose that the representative’s claim is true. and suppose that a sample of 20 dish owners is randomly selected. Assuming independence. what is the probability that (1) Nine or fewer dish owners in the sample subscribe to at least one premium movie channel? (2) More than ll dish owners in the sample subscribe to at least one premium movie channel‘? (3) Fewer than five dish owners in the sample subscribe to at least one premium movie channel? Question 5 A filling process is supposed to fill jars with 16 ounces of grape jelly. Specifications state that each jar must contain between 15.95 ounces and 16.05 ounces. Ajar is selected from the process every half hour until a sample of 100 jars is obtained. When the fills of the jars are measured, it is found that If = 16.0024 and 5 = D2454. Using X and s as point estimates of it and o, estimate the probability that a randomly selected jar will have a fill, .\'. that is out of specification. Assume that the process is stable and that the population of all jar fills is normally distributed.
