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Review Worksheet for Test 2 Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the following distribution to answer the question. 1) What is the total area under the curve? A) 2500 B) 3000 1) C) 1 D) 3 Apply the 68-95-99.7 rule to answer the question. 2) 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? A) 32% B) 68% C) 84% D) 95% 2) 3) 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? A) 98% B) 99.7% C) 95% D) 68% 3) 4) 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? A) 99.7% B) 68% C) 95% D) 34% 4) Find the indicated percentage for the normally distributed variable. Round your answer to two decimal places, if necessary. 5) The diameters of bolts produced by a certain machine are normally distributed with a mean of 5) 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.33 inches? A) 99.7% B) 99.87% C) 0.13% D) 50% 1 6) The volumes of soda in quart soda bottles are normally distributed with a mean of 32 ounces and a standard deviation of 1.2 ounces. What percentage of soda bottles will have a volume less than 31.70 ounces? A) 59.87% B) 43.10% C) 99.7% D) 40.13% 6) 7) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. What percentage of the ratings will be between 200 and 300? A) 97.72% B) 47.27% C) 47.72% D) 95% 7) 8) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. What percentage of the ratings will be between 170 and 220? A) 38.11% B) 95% C) 65.54% D) 27.43% 8) Find the requested percentile. 9) 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? A) Approximately 80th percentile B) Approximately 25th percentile C) Approximately 69th percentile D) Approximately 31th percentile 10) 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. A) 3.1 B) 2.9 C) 2.2 D) 3 Solve the problem. 11) Which of the following statements concerning areas under the standard normal distribution curve is/are true (if any)? a. The area to the left of -3 in a standard normal distribution curve is zero. b. The area under a standard normal distribution curve between any two z-scores is greater than zero. c. The area under the standard normal normal distribution curve between two z -scores will be negative if both z-scores are negative. d. The area under the standard normal distribution curve to the left of any z-score is less than 1. A) a B) a, c C) a, b D) b, d 12) Which of the following statements concerning areas under the standard normal distribution curve is/are true? a. If a z-score is negative, the area to its right is greater than 0.5 b. If the area to the right of a z-score is less than 0.5, the z-score is negative. c. If a z-score is positive, the area to its left is less than 0.5 A) a, c B) a, b C) b, c D) a 2 9) 10) 11) 12) 13) The area under the standard normal distribution curve between 1 and 2 is equal to 0.1359. Scores on a particular aptitude test are normally distributed with a mean of 100 and a standard deviation of 10. Which of the following are equal to 13.59%? a. The percentage of scores between 120 and 130 b. The percentage of scores between 110 and 120 c. The percentage of scores between 80 and 90 d. The percentage of scores between 90 and 120 e. The percentage of scores between 90 and 110 A) b B) b, c C) a, b D) e Find the requested mean or standard deviation. 14) 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? A) 60" B) 45" C) 30" D) 15" 15) The mean score on the exit examination for an urban high school is 63 with a standard deviation of 5. What is the mean of the resulting distribution of sample means for n = 9? A) 5 B) 63 C) 9 D) 21 13) 14) 15) 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. 16) A final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume that a 16) 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? A) 70% B) 0.38% C) 0.62% D) 30% 17) 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? A) 91.92% B) 5.48% C) 94.52% D) 8.08% 17) 18) The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.Assume that a random sample of 25 pregnant woman is selected and the mean is computer. What percentage of sample means will be between 259 and 277 days? A) 99.87% B) 99.74% C) 95.44% D) 0.13% 18) 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. 19) The amount of snowfall falling in a certain mountain range is normally distributed with a 19) 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 108.8 inches? A) 0.5808 B) 0.4192 C) 0.0808 D) 0.0026 3 20) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 106 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during 25 randomly picked years will be less than 108.8 inches? A) 0.5808 B) 0.9192 C) 0.4192 D) 0.0808 20) 21) The weights of the fish in a certain lake are normally distributed with a mean of 12 lb and a standard deviation of 6. If 4 fish are randomly selected, what is the likelihood that the mean weight will be between 9.6 and 15.6 lb? A) 0.6730 B) 0.3270 C) 0.0968 D) 0.4032 21) 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. 22) A multiple choice question has 14 possible answers, only one of which is correct. A student 22) makes a random guess on the question and is correct. A) statistically significant B) not statistically significant 23) Assume that a study of 500 randomly selected school bus routes showed that 476 of the buses arrived on time. One of the buses, however, was late. A) statistically significant B) not statistically significant Interpret the level of statistical significance for the event described. 24) A study of 600 college students taking Statistics 101 revealed that 58 students received the grade of A. Typically 10% of the class gets an A. The difference between this group of students and the expected value is not significant at the 0.05 level. What does this mean in this case? A) The probability that the difference occurred due to chance is more than 0.05. B) There is not enough information to make any conclusion. C) The probability that the difference occurred due to chance is less than 0.05. D) The probability of getting an A is 10% and only 9% got an A in this study. The difference is less than 5% so it is not significant. 23) 24) 25) A study of 600 college students taking Statistics 101 revealed that 59 students received the grade of A. Typically 10% of the class gets an A. The difference between this group of students and the expected value is not significant at the 0.05 level. What does this mean in this case? A) The probability of getting an A is 10% and only 9% got an A in this study. The difference is less than 5% so it is not significant. B) The probability that the difference occurred due to chance is more than 0.05. C) The probability that the difference occurred due to chance is less than 0.05. D) There is not enough information to make any conclusion. 25) 26) A study of students taking Statistics 101 was done. 500 students who studied for more than 10 hours averaged a B. 250 students who studied for less than 10 hours averaged a C. This difference was significant at the 0.01 level. What does this mean? A) The probability that the difference was due to chance alone is greater than 0.01. B) The improvement was due to the fact that more people studied. C) There is not enough information to make any conclusion. D) There is less than a 0.01 chance that the grades were better by chance alone. 26) 4 27) A study of students taking Statistics 101 was done. 400 students who studied for more than 10 hours averaged a B. 200 students who studied for less than 10 hours averaged a C. This difference was significant at the 0.01 level. What does this mean? A) The improvement was due to the fact that more people studied. B) There is less than a 0.01 chance that the grades were better by chance alone. C) The probability that the difference was due to chance alone is greater than 0.01. D) There is not enough information to make any conclusion. 27) 28) A national survey was done. It showed that a sample of 605 men aged 25-34 watched an average of 9 hours of television a week. A sample of 503 men aged 45-54 watched an average of 19 hours of television a week. This difference is significant at the 0.05 level. Interpret the result. A) The older group watches more television because they have more televisions. B) There is not enough information to make any conclusion. C) The probability that the difference was due to chance alone is greater than 0.05. D) The probability is less than 0.05 that the older group watches more television by chance alone. 28) Find the indicated probability. 29) If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least one head? 7 1 3 1 A) B) C) D) 8 4 4 2 29) 30) If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that the first two tosses come up the same? 1 1 1 3 A) B) C) D) 4 8 2 8 30) 31) 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.) 7 3 1 2 A) B) C) D) 10 5 2 5 31) 32) A bag contains four chips of which one is red, one is blue, one is green, and one is yellow. A chip is selected at random from the bag and then replaced in the bag. A second chip is then selected at random. Make a list of the possible outcomes (for example RB represents the outcome red chip followed by blue chip) and use your list to determine the probability that one blue chip and one yellow chip are selected. 1 1 1 1 A) B) C) D) 4 8 2 16 32) 5 33) 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? 1 A) 5 B) C) 0 D) 1 5 33) 34) A die with 12 sides is rolled. What is the probability of rolling a number less than 11? 5 1 11 A) B) C) D) 10 6 12 12 34) 35) In a poll, respondents were asked whether they had ever been in a car accident. 353 respondents indicated that they had been in a car accident and 140 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident? Round to the nearest thousandth, if necessary. A) 0.284 B) 2.521 C) 0.003 D) 0.716 35) Determine the probability of the given opposite event. 36) Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.178. Find the probability that in a given year it will not snow on January 1st in that town. A) 0.217 B) 1.178 C) 5.618 D) 0.822 37) 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 868 9313 What is the probability that a randomly selected degree is not in Mathematics? A) 0.907 B) 0.768 C) 0.820 D) 0.232 36) 37) Use the relative frequency method to estimate the probability. Round your answer to three decimal places. 38) A polling firm, hired to estimate the likelihood of the passage of an up-coming referendum, 38) 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 A) 0.6 B) 0.5 C) 0.4 6 D) 0.65 39) The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $75,000. 39) 91,000 107,000 67,000 115,000 71,000 91,000 75,000 59,000 131,000 171,000 123,000 71,000 107,000 99,000 75,000 139,000 55,000 99,000 63,000 83,000 A) 0.6 B) 0.4 C) 0.7 D) 0.8 40) The frequency table describes the distribution of birds viewed by a bird watching group. bird frequency wren 3 crow 6 hawk 2 goose 14 bluejay 1 40) Estimate the probability that the group will see a hawk on the next bird watching trip. A) 0.083 B) 0.077 C) 0.071 D) 0.308 Give the appropriate response. 41) Construct a table showing all possible outcomes and probabilities of tossing 3 fair coins at once. Tossing 3 Coins Coin 1 Coin 2 Coin 3 Outcome Probability A) Tossing 3 Coins Coin 1 Coin 2 Coin 3 Outcome Probability H H H HHH 1/8 H H T HHT 3/8 H T H HTH 3/8 H T T HTT 3/8 T H H THH 3/8 T H T THT 3/8 T T H TTH 3/8 T T T TTT 1/8 B) Tossing 3 Coins Coin 1 Coin 2 Coin 3 Outcome Probability H H H HHH 1/4 H H T HHT 1/4 T T H TTH 1/4 T T T TTT 1/4 7 41) C) Tossing 3 Coins Coin 1 Coin 2 Coin 3 Outcome Probability H H H HHH 1 H H T HHT 1 H T H HTH 1 H T T HTT 1 T H H THH 1 T H T THT 1 T T H TTH 1 T T T TTT 1 D) 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 8 42) Assume five fair coins are tossed at once. Construct a table showing the probability distribution for the events 5 heads, 4 heads, 3 heads, 2 heads, 1 head, and 0 heads.. 42) Tossing 5 Coins Result Probability Total A) Tossing 5 Coins Result Probability 5 heads 0 tails 1 4 heads 1 tail 5 3 heads 2 tails 10 2 heads 3 tails 10 1 head 4 tails 5 0 heads 5 tails 1 Total 32 B) Tossing 5 Coins Result Probability 5 heads 0 tails 1/6 4 heads 1 tail 1/6 3 heads 2 tails 1/6 2 heads 3 tails 1/6 1 head 4 tails 1/6 0 heads 5 tails 1/6 Total 1 C) Tossing 5 Coins Result Probability 5 heads 0 tails 1 4 heads 1 tail 1 3 heads 2 tails 1 2 heads 3 tails 1 1 head 4 tails 1 0 heads 5 tails 1 Total 6 D) Tossing 5 Coins Result Probability 5 heads 0 tails 1/32 4 heads 1 tail 5/32 3 heads 2 tails 10/32 2 heads 3 tails 10/32 1 head 4 tails 5/32 0 heads 5 tails 1/32 Total 1 Answer the question about the Law of Large Numbers. 43) 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. A) c B) b C) d D) a 43) Find the expected value. 44) In a game, you have a 1 22 probability of winning $108 and a probability of losing $9. What 23 23 is your expected value? A) $4.70 B) -$8.61 C) $13.30 9 D) -$3.91 44) 45) A contractor is considering a sale that promises a profit of $27,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $7000 with a probability of 0.3. What is the expected profit? A) $18,900 B) $23,800 C) $16,800 D) $20,000 45) 46) Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 1 or a 2, nothing otherwise. What is your expected value of your gain or loss? A) -$3.00 B) $3.00 C) $5.00 D) -$1.33 46) State whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative. 47) The number of hours one sleeps and the number of hours one is awake 47) A) Positive correlation B) Negative correlation C) Not correlated 48) The time it takes to read a book and the length of the book A) Positive correlation B) Negative correlation C) Not correlated 48) 49) Time spent rollerblading and distance covered A) Positive correlation B) Negative correlation C) Not correlated 49) Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram. 50) A) 0.5 B) -0.9 C) 0.9 50) D) -0.5 51) 51) A) 0.9 B) -0.6 C) 0.6 Solve the problem. 10 D) -0.1 52) The following table gives the total sales (revenue) and profits for 8 retailers. Construct a scatter diagram for the data and state whether sales and profits for these companies have no correlation, a positive correlation, or a negative correlation. Total Sales Profits Company (Millions of $) (Millions of $) Adams 9.5 0.5 Browns 22.0 1.4 Clay 35.0 1.8 Donners 64.0 3.0 Esters 27.5 0.9 Framer 45.0 2.6 Gillies 15.0 0.8 Hays 57.0 2.2 A) Positive correlation B) Positive correlation C) Negative correlation D) No correlation 11 52) Student TV Time Internet Time (hours) (hours) Tom 12 7 Dick 8 5 Harry 6 1 Sue 11 10 Betty 11 11 Erin 9 2 Jan 10 11 Internet Time (hours) 53) The table below shows the times (in hours) that seven students spend watching television and using the Internet. Construct a scatter diagram for the data and state whether these times have no correlation, a positive correlation, or a negative correlation. 24 22 20 18 16 14 12 10 8 6 4 2 y 2 4 6 8 10 12 14 16 18 20 22 24 x TV Time (hours) 24 22 20 18 16 14 12 10 8 6 4 2 B) Negative correlation y Internet Time (hours) Internet Time (hours) A) Positive correlation 24 22 20 18 16 14 12 10 8 6 4 2 2 4 6 8 10 12 14 16 18 20 22 24 x y 2 4 6 8 10 12 14 16 18 20 22 24 x TV Time (hours) TV Time (hours) 24 22 20 18 16 14 12 10 8 6 4 2 D) No correlation y Internet Time (hours) Internet Time (hours) C) Positive correlation 2 4 6 8 10 12 14 16 18 20 22 24 x 24 22 20 18 16 14 12 10 8 6 4 2 y 2 4 6 8 10 12 14 16 18 20 22 24 x TV Time (hours) TV Time (hours) 12 53) Provide an appropriate response. 54) How does the outlier affect the correlation coefficient?. A) The outlier reduces the correlation coefficient. B) The outlier has no effect on the correlation coefficient. C) None of the above D) The outlier increases the correlation coefficient. 13 54) Answer Key Testname: MATH 109 TEST 2 REVIEW 1) C 2) B 3) C 4) A 5) C 6) D 7) C 8) A 9) C 10) D 11) D 12) D 13) B 14) A 15) B 16) C 17) D 18) B 19) C 20) B 21) A 22) B 23) A 24) A 25) B 26) D 27) B 28) D 29) A 30) C 31) B 32) B 33) B 34) A 35) D 36) D 37) B 38) A 39) C 40) B 41) D 42) D 43) B 44) D 45) C 46) D 47) B 48) C 14 Answer Key Testname: MATH 109 TEST 2 REVIEW 49) 50) 51) 52) 53) 54) A C B B C A 15