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Chapter 6 Review A z-score is: a) b) c) d) The mean of the distribution The deviation from the mean divided by the standard deviation Always positive The standard error The mean score on a certain mathematics aptitude test is 72, with a standard deviation of 8.5. Assume a normal distribution of scores. If a student's z-score on the test is known to have been at the 25th percentile, what was the student’s actual score? 66.267 The life of Sunshine Stereo CD players is normally distributed with a mean of 2.3 years and a standard deviation of 0.4 year. What proportion of the players will break during the guarantee period of 2 years? 0.2266 The mean score on a certain mathematics test is 72 with a standard deviation of 8.5. Assume a normal distribution of scores. What score would one have to earn so that no more than 15% of the scores would be higher? 80.81 In a recent study it was found that in one town the number of hours that a typical 10year-old child watches television per week is evenly distributed with a median of 12 hours and a maximum of 15.5 hours. If Gary is a typical 10-year-old in this town, what is the probability that he watches between 9 and 14 hours? 0.7143 A traffic control engineer has found that the waiting time for a commuter in the Parker Road toll plaza of North Dallas Tollway during rush hour is approximately uniformly distributed with a mean of 8.7 minutes and a range of 5 minutes. What is the probability that the a randomly selected commuter will have to wait more than 10 minutes? 0.24 Which of the following statements are true? a) The area under a normal curve is T always equal to 1, no matter what the mean and standard deviation are. b) The larger the standard deviation of a normal curve, the taller and thinner the F curve. c) Normal curves with different means are T centered around different numbers. An electric circuit is designed so that voltage levels are uniformly distributed between 5.00V and 9.00V. Find the probability that a randomly selected voltage level is between 7.00V and 8.50V. .375 If heights of adult males are normally distributed with a mean of 70.2 inches and a standard deviation of 4.2 inches, and 95% of all adult males satisfy a minimum height requirement for police officers, what is that minimum height requirement? 63.29 inches Suppose that a distribution is shown to the right. P (x<1)= P (x>2) P (1<x<3)= .25 .375 .75 In studying ocean conditions, the Bureau of Fisheries found that for one location, the August water temperatures (in degrees Fahrenheit) were normally distributed with a mean of 83.6 and a standard deviation of 2.4. Find the temperature that is exceeded 10% of the time. 86.68°F A service station is located at one end of a 4kilometer tunnel. Any vehicle breakdown requires servicing is equally likely to occur at any point in the tunnel. What is the probability that a service call will involve a vehicle located in the first 1.8 km? What is the probability that a service call will involve a vehicle located at least halfway in the tunnel? a) .45 b) .5