1) What is the total area under the curve? 1) 2) What is the mean of the distribution? 2)

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1 Math 1090 Test 2 Review Worksheet Ch5 and Ch 6 Name Use the following distribution to answer the question. 1) What is the total area under the curve? 1) 2) What is the mean of the distribution? 2) 3) Estimate (using area) the relative frequency of values greater than 2000 hours. 3) 4) Estimate the percentage of light bulbs having a life less than 2500 hours. 4) 5) Estimate the percentage of light bulbs having a life between 2000 hours and 3000 hours. 5) Apply the rule to answer the question. 6) The lifetimes of light bulbs of a particular type are normally distributed with a mean of 390 hours and a standard deviation of 6 hours. What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean? 6) 7) The lifetimes of light bulbs of a particular type are normally distributed with a mean of 210 hours and a standard deviation of 8 hours. What percentage of the bulbs have lifetimes that lie within 2 standard deviations to either side of the mean? 7) 8) The systolic blood pressure of a group of 18-year-old women is normally distributed with a mean of 111 mmhg and a standard deviation of 12 mmhg. What percentage of 18-year-old women in this group have a systolic blood pressure that lies within 3 standard deviations to either side of the mean? 8) 1

2 Find the indicated percentage for the normally distributed variable. Round your answer to two decimal places, if necessary. 9) The volumes of soda in quart soda bottles are normally distributed with a mean of 32 9) ounces and a standard deviation of 1.2 ounces. What percentage of soda bottles will have a volume less than ounces? Find the requested percentile. 10) One college requires that scholarship students maintain a GPA of 3.3, when the GPAs at that college are normally distributed with a mean of 3.0 and a standard deviation of 0.6. What percentile must scholarship students remain in? 10) 11) At one college, GPA's are normally distributed with a mean of 2.6 and a standard deviation of 0.6. Find the 75th percentile. Round your answer to one decimal place. 11) Find the requested mean or standard deviation. 12) The heights of a large population of students have a mean of 60" with a standard deviation of 3". What is the mean of the resulting distribution of sample means for n =16? 12) 13) The heights of a large population of students have a mean of 62" with a standard deviation of 4". What is the standard deviation of the resulting distribution of sample means for n =16? 13) Solve the problem. Round the standard score to the nearest tenth before using the z-score tables. Express your answer as a percent rounded to hundredths of a percent. 14) A final exam in Math 160 has a mean of 73 with standard deviation Assume that a 14) random sample of 24 students is selected and the test score of the sample is computed. Assuming the scores are normally distributed, what percentage of sample means are less than 69? 15) A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.77 hours. Assume that a random sample of 40 mechanics is selected and the mean rebuild time of the sample is computed. Assuming the rebuilding times are normally distributed, what percentage of sample means are greater than 8.8 hours? 15) Solve the problem. Round the standard score to the nearest tenth before using the z-score tables. Express your answer as a decimal rounded to four decimal places. 16) The amount of snowfall falling in a certain mountain range is normally distributed with a 16) mean of 106 inches, and a standard deviation of 12 inches. What is the likelihood that the mean annual snowfall during 36 randomly picked years will exceed inches? 2

3 For the given event, state whether the difference between what occurred and what you would have expected by chance is statistically significant or not statistically significant. 17) Assume that a study of 500 randomly selected school bus routes showed that 476 of the 17) buses arrived on time. One of the buses, however, was late. Find the indicated probability. 18) A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that D is included in the sample. (Hint: There are 10 possible samples.) 18) 19) On a multiple choice test, each question has 5 possible answers. If you make a random guess on the first question, what is the probability that you are correct? 19) 20) A bag contains 6 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? 20) 21) Suppose you randomly select a family with three children. Assume that births of boys and girls are equally likely. What is the probability that the family has at least two girls? 21) Determine the probability of the given opposite event. 22) If P(A) = 9, find P(A). 22) 11 23) The distribution of B.A. degrees conferred by a local college is listed below, by major. Major Frequency English 2073 Mathematics 2164 Chemistry 318 Physics 856 Liberal Arts 1358 Business 1676 Engineering What is the probability that a randomly selected degree is not in Mathematics? 23) 3

4 Use the relative frequency method to estimate the probability. Round your answer to three decimal places. 24) A polling firm, hired to estimate the likelihood of the passage of an up-coming 24) referendum, obtained the set of survey responses to make its estimate. The encoding system for the data is: 1 = FOR, 2 = AGAINST. If the referendum were held today, estimate the probability that it would pass. 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1 25) In a certain class of students, there are 9 boys from Wilmette, 3 girls from Winnetka, 6 girls from Wilmette, 6 boys from Glencoe, 3 boys from Winnetka and 4 girls from Glencoe. If the teacher calls upon a student to answer a question, what is the probability that the student will be a boy? 25) Give the appropriate response. 26) Construct a table showing all possible outcomes and probabilities of tossing 3 fair coins at once. 26) Coin 1 Tossing 3 Coins Coin 2 Coin 3 Outcome Probability Answer the question about the Law of Large Numbers. 27) A fair coin is tossed 5000 times. What can you say about getting the outcome of exactly 2500 tails? a. Since the probability of a tail is 0.5 for each toss, you should expect exactly 2500 tails in 5000 tosses. b. You should not expect exactly 2500 tails in 5000 tosses, but the proportion of tails should approach 0.5 as the number of tosses increases. c. You should expect between 2400 and 2600 tails in 5000 tosses. d. Getting 2500 tails is no more likely than getting any other number of tails in 5000 tosses. 27) Find the expected value. 28) In a game, you have a 1 23 What is your expected value? 22 probability of winning $108 and a probability of losing $ ) 29) A 28-year-old man pays $98 for a one-year life insurance policy with coverage of $ 140,000. If the probability that he will live through the year is , what is the expected value for the insurance policy? 29) 30) Suppose that you arrive at a bus stop randomly, so all arrival times are equally likely. The bus arrives regularly every 50 minutes without delay. What is the expected value of your waiting time? A) 20 min B) 1 min C) 10 min D) 25 min 30) 4

5 Answer Key Testname: 1) 1 2) ) ) 50% 5) 70% 6) 68% 7) 95% 8) 99.7% 9) 40.13% 10) Approximately 69th percentile 11) 3 12) 60" 13) 1" 14) 0.62% 15) 8.08% 16) ) statistically significant 18) ) ) ) ) 11 23) ) ) ) Tossing 3 Coins Coin 1 Coin 2 Coin 3 Outcome Probability H H H HHH 1/8 H H T HHT 1/8 H T H HTH 1/8 H T T HTT 1/8 T H H THH 1/8 T H T THT 1/8 T T H TTH 1/8 T T T TTT 1/8 27) b 28) -$ ) $ ) D 5