Math 227 (Statistics) Chapter 6 Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the 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 3? 1) A) 0.750 B) 0.575 C) 0.625 D) 0.500 2) What is the probability that the random variable has a value between 4.5 and 7.7? 2) A) 0.5250 B) 0.4000 C) 0.6500 D) 0.2750 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. 3) Less than 9 pounds 3) A) 1 2 B) 5 7 C) 1 3 D) 1 6 4) Between 7 pounds and 10 pounds 4) A) 1 4 B) 1 3 C) 2 3 D) 1 2 If Z is a standard normal variable, find the probability. 5) The probability that Z lies between 0 and 3.01 5) A) 0.4987 B) 0.1217 C) 0.9987 D) 0.5013 6) The probability that Z is less than 1.13 6) A) 0.8708 B) 0.1292 C) 0.8907 D) 0.8485 7) P(Z > 0.59) 7) A) 0.2224 B) 0.2776 C) 0.7224 D) 0.2190 8) P(-0.73 < Z < 2.27) 8) A) 0.4884 B) 0.2211 C) 0.7557 D) 1.54 The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0 C at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0 C (denoted by negative numbers) and some give readings above 0 C (denoted by positive numbers). Assume that the mean reading is 0 C and the standard deviation of the readings is 1.00 C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information. 9) Find P96, the 96th percentile. 9) A) 1.03 B) 1.82 C) 1.75 D) -1.38 10) Find P40, the 40th percentile. 10) A) 0.57 B) -0.25 C) 0.25 D) -0.57 1
11) If 9% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others. A) 1.45 B) 1.26 C) 1.39 D) 1.34 12) If 6.3% of the thermometers are rejected because they have readings that are too high and another 6.3% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others. A) -1.46, 1.46 B) -1.45, 1.45 C) -1.53, 1.53 D) -1.39, 1.39 11) 12) 13) For a standard normal distribution, find the percentage of data that are more than 1 standard deviation away from the mean. A) 34.13% B) 15.87% C) 68.26% D) 31.74% 14) For a standard normal distribution, find the percentage of data that are between 3 standard deviations below the mean and 1 standard deviation above the mean. A) 16.00% B) 99.74% C) 84.00% D) 15.74% 15) Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(-a < z < a) = 0.4314, find a. A) -0.18 B) 0.57 C) 0.3328 D) 1.49 16) Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z > c) = 0.1093, find c. A) 0.4562 B) 0.27 C) -1.23 D) 1.23 13) 14) 15) 16) Assume that X has a normal distribution, and find the indicated probability. 17) The mean is µ = 60.0 and the standard deviation is = 4.0. Find the probability that X is less than 53.0. A) 0.9599 B) 0.0802 C) 0.0401 D) 0.5589 18) The mean is µ = 15.2 and the standard deviation is = 0.9. Find the probability that X is greater than 15.2. A) 1.0000 B) 0.5000 C) 0.9998 D) 0.0003 19) The mean is µ = 15.2 and the standard deviation is = 0.9. Find the probability that X is between 14.3 and 16.1. A) 0.8413 B) 0.1587 C) 0.3413 D) 0.6826 17) 18) 19) 20) 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) 1148.1 B) 1078.3 C) 1087.8 D) 1021.7 21) Human body temperatures are normally distributed with a mean of 98.20 F and a standard deviation of 0.62 F. Find the temperature that separates the top 7% from the bottom 93%. A) 99.12 F B) 97.28 F C) 98.78 F D) 98.40 F 20) 21) 2
22) The serum cholesterol levels for men in one age group are normally distributed with a mean of 178.1 and a standard deviation of 40.7. All units are in mg/100 ml. Find the two levels that separate the top 9% and the bottom 9%. A) 165.1 mg/100ml and 191.12 mg/100ml B) 161.4 mg/100ml and 194.8 mg/100ml C) 123.6 mg/100ml and 232.6 mg/100ml D) 107.3 mg/100ml and 248.9 mg/100ml 22) Find the indicated probability. 23) 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) 37.45% B) 2.28% C) 47.72% D) 97.72% 24) 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) 0.1554 B) 0.3811 C) 0.2257 D) 0.0703 23) 24) 25) Scores on a test have a mean of 62 and Q3 is 84. The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth. A) 32.8 B) 29.3 C) 16.5 D) 14.7 26) Scores on a test have a mean of 73 and Q3 is 80. The scores have a distribution that is approximately normal. Find P90. (You will need to first find the standard deviation.) A) 85.3 B) 86.8 C) 85.7 D) 86.4 27) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 74 inches, and a standard deviation of 12 inches. What is the probability that the mean annual snowfall during 36 randomly picked years will exceed 76.8 inches? A) 0.5808 B) 0.4192 C) 0.0026 D) 0.0808 28) 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 29) 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 less than 76. A) 0.0301 B) 0.9699 C) 0.8962 D) 0.9203 25) 26) 27) 28) 29) Use the continuity correction and describe the region of the normal curve that corresponds to the indicated binomial probability. 30) The probability of more than 56 correct answers 30) A) The area to the right of 55.5 B) The area to the right of 56 C) The area to the right of 56.5 D) The area to the left of 56.5 31) The probability of at least 49 boys 31) A) The area to the left of 48.5 B) The area to the right of 49 C) The area to the right of 48.5 D) The area to the right of 49.5 3
32) The probability of fewer than 43 democrats 32) A) The area to the left of 43.5 B) The area to the right of 43.5 C) The area to the left of 43 D) The area to the left of 42.5 33) The probability of exactly 37 green marbles 33) A) The area between 36.5 and 37.5 B) The area between 36.5 and 38.5 C) The area between 37 and 37.5 D) The area between 36.5 and 37 34) The probability of no more than 71 defective CD's 34) A) The area to the left of 71.5 B) The area to the right of 71.5 C) The area to the left of 70.5 D) The area to the left of 71 35) The probability that the number of correct answers is between 16 and 38 inclusive 35) A) The area between 15.5 and 38.5 B) The area between 15.5 and 37.5 C) The area between 16 and 38 D) The area between 16.5 and 37.5 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. 36) n = 18 and p =.6 36) A) Normal approximation is suitable. B) Normal approximation is not suitable. 37) n = 16 and p =.8 37) A) Normal approximation is suitable. B) Normal approximation is not suitable. 38) n = 38 and p =.9 38) A) Normal approximation is not suitable. B) Normal approximation is suitable. Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. 39) A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is 39) correct. If all answers are random guesses, estimate the probability of getting at least 20% correct. A) 0.0901 B) 0.8508 C) 0.1492 D) 0.3508 40) A certain question on a test is answered correctly by 22% of the respondents. Estimate the probability that among the next 150 responses there will be at most 40 correct answers. A) 0.8997 B) 0.1003 C) 0.9306 D) 0.0694 41) 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. A) 0.0832 B) 0.5871 C) 0.4168 D) 0.4641 42) In one county, the conviction rate for speeding is 85%. Estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions. A) 0.0420 B) 0.8962 C) 0.1038 D) 0.3962 43) The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate. A) 0.9331 B) 0.0769 C) 0.0669 D) 0.0679 40) 41) 42) 43) 4
Use the normal distribution to approximate the desired probability. 44) A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 11 tosses. What is the probability of being correct 11 or more times by guessing? Does this probability seem to verify her claim? A).4129, yes B).0871, no C).4129, no D).0871, yes 45) A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 16 tosses. What is the probability of being correct 16 or more times by guessing? Does this probability seem to verify her claim? A).4931, yes B).0069, yes C).4931, no D).0069, no 44) 45) 46) Find the probability that in 200 tosses of a fair die, we will obtain at least 40 fives. 46) A).2229 B).0871 C).1210 D).3871 47) Find the probability that in 200 tosses of a fair die, we will obtain at exactly 30 fives. 47) A).0871 B).1871 C).0429 D).0619 48) Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives. 48) A).1871 B).4936 C).2946 D).3229 5