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CHOICE. Exam Name___________________________________ MULTIPLE Choose the one alternative that best completes the statement or answers the question. Determine whether the given procedure results in a binomial distribution. If not, state the reason why. 1) Spinning a roulette wheel 6 times, keeping track of the occurrences of a winning number of "16". A) Procedure results in a binomial distribution.. B) Not binomial: there are more than two outcomes for each trial. C) Not binomial: the trials are not independent. D) Not binomial: there are too many trials. Solve the problem. 2) On a multiple choice test with 18 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the variance for the number of correct answers. A) 33.8 B) 11.4 C) 1.8 D) 3.4 Find the indicated mean. 3) A certain rare form of cancer occurs in 32 children in a million, so its probability is 0.000032. In the city of Normalville there are 76,430,000 children. A Poisson distribution will be used to approximate the probability that the number of cases of the disease in Normalville children is more than 2. Find the mean of the appropriate Poisson distribution (the mean number of cases in groups of 76,430,000 children). A) 245 B) 2450 C) 24,500 D) 0.000032 1) 2) 3) Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 4) Shaded area is 0.0694. 4) A) 1.45 B) 1.39 C) 1.26 D) 1.48 Solve the problem. Round to the nearest tenth unless indicated otherwise. 5) The serum cholesterol levels for men in one age group are normally distributed with a mean of 178.3 and a standard deviation of 40.4. All units are in mg/100 mL. Find the two levels that separate the top 9% and the bottom 9%. A) 124.2 mg/100mL and 232.4 mg/100mL B) 108.0 mg/100mL and 248.6 mg/100mL C) 165.4 mg/100mL and 191.23 mg/100mL D) 161.7 mg/100mL and 194.9 mg/100mL Solve the problem. 6) Human body temperatures are normally distributed with a mean of 98.20F and a standard deviation of 0.62F. If 19 people are randomly selected, find the probability that their mean body temperature will be less than 98.50F. A) 0.4826 B) 0.3343 C) 0.0833 D) 0.9826 1 5) 6) Find the indicated critical z value. 7) Find the critical value z /2 that corresponds to a 98% confidence level. A) 1.75 B) 2.575 C) 2.33 7) D) 2.05 Do one of the following, as appropriate: (a) Find the critical value z /2, (b) find the critical value t /2, (c) state that neither the normal nor the t distribution applies. 8) 95%; n = 11; is known; population appears to be very skewed. 8) A) z /2 = 1.96 B) z /2 = 1.812 C) t /2 = 2.228 D) Neither the normal nor the t distribution applies. Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 9) In a random sample of 184 college students, 97 had part-time jobs. Find the margin of error for the 9) 95% confidence interval used to estimate the population proportion. A) 0.126 B) 0.00266 C) 0.0649 D) 0.0721 Express the confidence interval using the indicated format. ^ 10) Express the confidence interval (0.668, 0.822) in the form of p E. A) 0.745 0.154 B) 0.668 0.077 C) 0.668 0.154 D) 0.745 0.077 10) Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 11) Of 234 employees selected randomly from one company, 12.82% of them commute by carpooling. 11) Construct a 90% confidence interval for the true percentage of all employees of the company who carpool. A) 9.23% < p < 16.4% B) 7.18% < p < 18.5% C) 8.54% < p < 17.1% D) 7.73% < p < 17.9% Solve the problem. Round the point estimate to the nearest thousandth. 12) Find the point estimate of the proportion of people who wear hearing aids if, in a random sample of 304 people, 20 people had hearing aids. A) 0.066 B) 0.934 C) 0.062 D) 0.063 12) Use the given data to find the minimum sample size required to estimate the population proportion. ^ ^ 13) Margin of error: 0.04 ; confidence level: 94%; p and q unknown A) 587 B) 572 C) 486 D) 553 13) Use the given degree of confidence and sample data to construct a confidence interval for the population mean . Assume that the population has a normal distribution. 14) n = 10, x = 8.7, s = 3.3, 95% confidence A) 6.79 < < 10.61 B) 6.35 < < 11.05 C) 6.34 < < 11.06 D) 6.37 < < 11.03 Solve the problem. 15) A simple random sample of women aged 18-24 is selected, and the systolic blood pressure of each woman is measured. The results (in mmHg) are as follows: x = 122.0, s = 14.7. The sample size is less than 20. A 99% confidence interval for the population mean is found to be = 122.0 10.41. Find the sample size. A) 14 B) 15 C) 16 D) 17 2 14) 15) Assume that a sample is used to estimate a population mean . Use the given confidence level and sample data to find the margin of error. Assume that the sample is a simple random sample and the population has a normal distribution. Round your answer to one more decimal place than the sample standard deviation. _ 16) 95% confidence; n = 91; x = 16, s = 9.1 16) A) 1.90 B) 1.63 C) 1.71 D) 4.10 Do one of the following, as appropriate: (a) Find the critical value z /2, (b) find the critical value t /2, (c) state that neither the normal nor the t distribution applies. 17) 98%; n = 7; = 27; population appears to be normally distributed. 17) A) z /2 = 2.05 B) t /2 = 2.575 C) z /2 = 2.33 D) t /2 = 1.96 Use the confidence level and sample data to find a confidence interval for estimating the population . Round your answer to the same number of decimal places as the sample mean. 18) 37 packages are randomly selected from packages received by a parcel service. The sample has a 18) mean weight of 17.0 pounds and a standard deviation of 3.3 pounds. What is the 95% confidence interval for the true mean weight, , of all packages received by the parcel service? A) 16.1 lb < < 17.9 lb B) 15.6 lb < < 18.4 lb C) 15.9 lb < < 18.1 lb D) 15.7 lb < < 18.3 lb 19) A random sample of 130 full-grown lobsters had a mean weight of 21 ounces and a standard deviation of 3.0 ounces. Construct a 98% confidence interval for the population mean . A) 21 oz < < 23 oz B) 19 oz < < 21 oz C) 20 oz < < 22 oz D) 20 oz < < 23 oz 19) 20) A random sample of 105 light bulbs had a mean life of x = 441 hours with a standard deviation of = 40 hours. Construct a 90% confidence interval for the mean life, , of all light bulbs of this type. A) 432 hr < < 450 hr B) 435 hr < < 447 hr C) 431 hr < < 451 hr D) 433 hr < < 449 hr 20) Solve the problem. 21) A 99% confidence interval (in inches) for the mean height of a population is 65.3 < < 66.9. This result is based on a sample of size 144. Construct the 95% confidence interval. (Hint: you will first need to find the sample mean and sample standard deviation). A) 65.4 in < < 66.8 in. B) 65.6 in < < 66.6 in. C) 65.5 in < < 66.7 in. D) 65.2 in < < 67.0 in. 21) 22) 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 78. A) 0.0008 B) 0.0036 C) 0.8962 D) 0.0103 22) 23) A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.7 hours. A) 0.1469 B) 0.1285 C) 0.1346 D) 0.1946 23) 3 24) Assume that women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 90 women are randomly selected, find the probability that they have a mean height between 62.9 inches and 64.0 inches. A) 0.9318 B) 0.7248 C) 0.0424 D) 0.1739 24) 25) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 107 inches, and a standard deviation of 12 inches. What is the probability that the mean annual precipitation 36 during randomly picked years will be less than 109.8 inches? A) 0.9192 B) 0.5808 C) 0.4192 D) 0.0808 25) 26) A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 7.7 hours. A) 0.9634 B) 0.9931 C) 0.8531 D) 0.9712 26) 27) In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. If 50 different homes are randomly selected, find the probability that their mean energy consumption level for September is greater than 1075 kWh. A) 0.4562 B) 0.0438 C) 0.2090 D) 0.2910 27) 28) The scores on a certain test are normally distributed with a mean score of 43 and a standard deviation of 3. What is the probability that a sample of 90 students will have a mean score of at least 43.3162? A) 0.3413 B) 0.3174 C) 0.1587 D) 0.8413 28) Solve the problem. Round to the nearest tenth unless indicated otherwise. 29) 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%. A) 7.8 years B) 10.5 years C) 9.8 years D) 11.2 years Find the indicated probability. 30) The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches? A) 47.72% B) 37.45% C) 97.72% D) 2.28% Solve the problem. Round to the nearest tenth unless indicated otherwise. 31) In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. Find P45, which is the consumption level separating the bottom 45% from the top 55%. A) 1021.7 B) 1148.1 C) 1078.3 Provide an appropriate response. 32) Find P15, which is the IQ score separating the bottom 15% from the top 85%. A) 82.5 B) 84.6 C) 84.0 4 29) 30) 31) D) 1087.8 32) D) 83.3 Find the indicated probability. 33) 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. If an applicant is randomly selected, find the probability of a rating that is between 170 and 220. A) 0.0703 B) 0.1554 C) 0.3811 D) 0.2257 Solve the problem. 34) 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.) A) 87 B) 77 C) 86 D) 84 33) 34) Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 35) 35) A) 0.7198 B) 0.8599 C) 0.2802 D) 0.1401 Using the following uniform density curve, answer the question. 36) What is the probability that the random variable has a value greater than 2? A) 0.700 B) 0.625 C) 0.750 Solve the problem. 37) In a continuous uniform distribution, minimum + maximum = and 2 D) 0.875 36) 37) range = 12 Find the mean and standard deviation for a uniform distribution having a minimum of - 4 and a maximum of 11. A) =7.5, = 4.33 B) = 3.5, = 4.33 C) =3.5, = 2.02 If z is a standard normal variable, find the probability. 38) P(-0.73 < z < 2.27) A) 0.2211 B) 0.7557 C) 0.4884 5 D) 1.54 38) Use the Poisson Distribution to find the indicated probability. 39) A naturalist leads whale watch trips every morning in March. The number of whales seen has a Poisson distribution with a mean of 1.8. Find the probability that on a randomly selected trip, the number of whales seen is 4. A) 0.2892 B) 0.1229 C) 0.4338 D) 0.0723 Use the Poisson model to approximate the probability. Round your answer to four decimal places. 40) The probability that a car will have a flat tire while driving through a certain tunnel is 0.00007. Use the Poisson distribution to approximate the probability that among 10,000 cars passing through this tunnel, at least one will have a flat tire. A) 0.3476 B) 0.8558 C) 0.5034 D) 0.4966 E) 0.6524 Provide an appropriate response. 41) Assume that x is a random variable in a probability distribution with mean and standard deviation . Find expressions for the mean and standard deviation if every value of x is modified by first being multiplied by 6, then increased by 5 . A) new = + 5; new =6 B) new = 6 + 5 ; new =6 C) new = 6 + 5; new = 6 D) new =5 + 6; +5 39) 40) 41) new = 5 Use the Poisson Distribution to find the indicated probability. 42) The town of Fastville has been experiencing a mean of 68.7 car accidents per year. Find the probability that on a given day the number of car accidents in Fastville is 3. (Assume 365 days in a year.) A) 0.000801 B) 0.00103 C) 0.000120 D) 0.000921 Solve the problem. 43) A company manufactures batteries in batches of 18 and there is a 3% rate of defects. Find the mean number of defects per batch. A) 54 B) 0.5 C) 5.4 D) 17.5 44) The probability is 0.2 that a person shopping at a certain store will spend less than $20. For groups of size 17, find the mean number who spend less than $20. A) 4.0 B) 16.0 C) 3.4 D) 13.6 42) 43) 44) Use the given values of n and p to find the minimum usual value - 2 and the maximum usual value + 2 . Round your answer to the nearest hundredth unless otherwise noted. 45) n = 267, p = 0.239 Round your answers to the nearest thousandth. 45) A) Minimum: 53.958; maximum: 73.668 B) Minimum: 77.75; maximum: 49.876 C) Minimum: 56.844; maximum: 70.782 D) Minimum: 49.876; maximum: 77.75 Solve the problem. 46) A die is rolled 9 times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos. A) 3 B) 2.25 C) 1.5 D) 7.5 Find the indicated probability. 47) An archer is able to hit the bull's-eye 53% of the time. If she shoots 10 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others. A) 0.179 B) 0.0789 C) 0.000851 D) 0.0905 6 46) 47) Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. 48) n =12, x = 5, p = 0.25 48) A) 0.103 B) 0.082 C) 0.091 D) 0.027 Determine whether the given procedure results in a binomial distribution. If not, state the reason why. 49) Choosing 10 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time without replacement, keeping track of the number of red marbles chosen. A) Not binomial: there are too many trials. B) Procedure results in a binomial distribution. C) Not binomial: the trials are not independent. D) Not binomial: there are more than two outcomes for each trial. Find the indicated probability. 50) A multiple choice test has 7 questions each of which has 4 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 3 questions correctly? A) 0.0156 B) 0.173 C) 0.311 D) 0.827 51) A tennis player makes a successful first serve 48% of the time. If she serves 9 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others. A) 0.111 B) 0.00219 C) 0.184 D) 0.0853 49) 50) 51) Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. 52) n = 64, x = 3, p = 0.04 52) A) 0.139 B) 0.375 C) 0.221 D) 0.091 7 ... View Full Document