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Exam Name___________________________________ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Using the following uniform density curve, answer the question. 1) What is the probability that the random variable has a value greater than 2? 1) Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost. 2) More than 11 pounds 2) Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 3) 3) -2.36-1.77-1.18-0.59 0.59 1.18 1.77 2.36 z Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 4) Shaded area is 0.0901. 4) z If z is a standard normal variable, find the probability. 5) The probability that z lies between 0.7 and 1.98 5) 6) P(-0.73 < z < 2.27) 6) Solve the problem. 7) For a standard normal distribution, find the percentage of data that are more than 2 standard deviations below the mean or more than 3 standard deviations above the mean. 1 7) Solve the problem. Round to the nearest tenth unless indicated otherwise. 8) The amount of rainfall in January in a certain city is normally distributed with a mean of 4.3 inches and a standard deviation of 0.3 inches. Find the value of the quartile Q1. 9) Suppose that replacement times for washing machines are normally distributed with a mean of 9.5 years and a standard deviation of 1.8 years. Find the replacement time that separates the top 18% from the bottom 82%. Find the indicated probability. 10) The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days? 11) The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter of a randomly selected pencil will be less than 0.285 inches? Solve the problem. 12) A math teacher gives two different tests to measure students' aptitude for math. Scores on the first test are normally distributed with a mean of 23 and a standard deviation of 4.2. Scores on the second test are normally distributed with a mean of 71 and a standard deviation of 10.8. Assume that the two tests use different scales to measure the same aptitude. If a student scores 29 on the first test, what would be his equivalent score on the second test? (That is, find the score that would put him in the same percentile.) 8) 9) 10) 11) 12) 13) A baseball player has a batting average of 0.346, so the probability of a hit is 0.346. Assume that his hitting attempts are independent of each other. Assume that the batter gets up to bat 4 times in each game. Estimate the probability that in 50 consecutive games, there are at least 45 games in which the batter gets at least one hit. (Hint: first find the probability that in one game the batter gets at least one hit) 13) 14) In a game of roulette, Jorge places 170 bets of $1 each on the number 3. A win pays off with odds 35:1 and on any one spin there is a 1/38 probability that 3 will be the winning number. Among the 170 bets, what is the minimum number of wins needed for Jorge to make a profit? Estimate the probability that Jorge will make a profit. 14) 15) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is greater than 71. 15) 16) Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. If 19 people are randomly selected, find the probability that their mean body temperature will be less than 98.50°F. 16) The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. 17) The probability that the number of correct answers is between 18 and 45 inclusive 17) 18) The probability of more than 33 correct answers 18) 2 19) The probability of at least 35 boys 19) 20) The probability of fewer than 49 democrats 20) 21) The probability of exactly 36 green marbles 21) 22) The probability of no more than 64 defective CD's 22) 23) The probability that the number of correct answers is between 18 and 48 inclusive 23) For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. 24) n = 22 and p = 0.6 24) 25) n = 19 and p = 0.8 25) 26) n = 19 and p = 0.5 26) 27) n = 17 and p = 0.2 27) 28) n = 63 and p = 0.7 28) 29) n = 33 and p = 0.9 29) Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. 30) Estimate the probability of getting exactly 43 boys in 90 births. 30) 31) A product is manufactured in batches of 120 and the overall rate of defects is 5%. Estimate the probability that a randomly selected batch contains more than 6 defects. Use the normal distribution to approximate the desired probability. 32) Merta reports that 74% of its trains are on time. A check of 60 randomly selected trains shows that 38 of them arrived on time. Find the probability that among the 60 trains, 38 or fewer arrive on time. Based on the result, does it seem plausible that the "on-time" rate of 74% could be correct? 3 31) 32) Solve the problem. 33) A normal quartile plot is given below for a sample of scores on an aptitude test. Use the plot to assess the normality of scores on this test. Explain your reasoning. 4 33) Answer Key Testname: CHAPTER 6 REVIEW 1) 0.750 2) 1 6 3) 0.2776 4) -1.34 5) 0.2181 6) 0.7557 7) 2.41% 8) 4.1 9) 11.2 years 10) 0.0166 11) 0.0668 12) 86 13) 0.0918 14) 5; 0.496 15) 0.8962 16) 0.9826 17) The area between 17.5 and 45.5 18) The area to the right of 33.5 19) The area to the right of 34.5 20) The area to the left of 48.5 21) The area between 35.5 and 36.5 22) The area to the left of 64.5 23) The area between 17.5 and 48.5 24) Normal approximation is suitable. 25) Normal approximation is not suitable. 26) Normal approximation is suitable. 27) Normal approximation is not suitable. 28) Normal approximation is suitable. 29) Normal approximation is not suitable. 30) 0.0764 31) 0.4168 32) 0.0409, no 33) Since the normal quartile plot is roughly linear, it appears that scores on this test are approximately normally distributed. 5