Math 201 Week 5 Online Test Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 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. 1 1) n = 4, x = 3, p = 1) 6 A) 0.015 2) n = 5, x = 2, p = 0.70 A) 0.464 B) 0.023 C) 0.012 D) 0.004 2) B) 0.700 C) 0.198 D) 0.132 Find the indicated probability. Round to three decimal places. 3) A machine has 12 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working. A) 0.133 B) 0.927 C) 0.795 D) 0.206 3) 4) A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 22 components and accept the whole batch if there are fewer than 3 defectives. If a particular shipment of thousands of components actually has a 7% rate of defects, what is the probability that this whole shipment will be accepted? A) 0.803 B) 0.265 C) 0.601 D) 0.133 4) 5) In a study, 43% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 13 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 13 adults are randomly selected, 3 or fewer are in excellent health. A) 0.077 B) 0.037 C) 0.119 D) 0.082 5) Find the indicated probability. 6) The brand name of a certain chain of coffee shops has a 54% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 10 Coffleton residents. Find the probability that exactly 4 of the 10 Coffleton residents recognize the brand name. A) 0.0850 B) 0.0824 C) 0.000806 D) 0.169 Use the Poisson Distribution to find the indicated probability. 7) If the random variable x has a Poisson Distribution with mean = 6, find the probability that x = 2. A) 0.04462 B) 0.12128 C) 0.05577 D) 0.01487 1 6) 7) Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 8) 8) -1.82 z 1.82 A) 0.4656 B) -0.0344 C) 0.0344 D) 0.9656 9) 9) -1.84 -0.92 A) 0.6424 0.92 z 1.84 B) 0.3576 C) 0.1788 D) 0.8212 10) 10) -2.34 -1.17 A) 0.2420 1.17 2.34 z B) 0.8790 C) 0.1210 D) 0.7580 Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 11) Shaded area is 0.0694. 11) z A) 1.45 B) 1.48 If z is a standard normal variable, find the probability. 12) The probability that z lies between -2.41 and 0 A) 0.0948 B) 0.4910 C) 1.26 D) 1.39 C) 0.5080 D) 0.4920 C) 0.8708 D) 0.1292 12) 13) The probability that z is less than 1.13 A) 0.8485 B) 0.8907 13) 2 14) P(z < 0.97) A) 0.8315 14) B) 0.1660 C) 0.8078 D) 0.8340 The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0C 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 0C (denoted by negative numbers) and some give readings above 0C (denoted by positive numbers). Assume that the mean reading is 0C and the standard deviation of the readings is 1.00C. 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. 15) Find Q3, the third quartile. 15) A) 0.82 B) 0.53 C) 0.67 D) -1.3 16) A quality control analyst wants to examine thermometers that give readings in the bottom 4%. Find the reading that separates the bottom 4% from the others. A) -1.63 B) -1.75 C) -1.48 D) -1.89 Provide an appropriate response. 17) Find the indicated IQ score. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). The shaded area under the curve is 0.5675. A) 110.7 B) 129.6 C) 97.5 Solve the problem. Round to the nearest tenth unless indicated otherwise. 19) Scores on a test are normally distributed with a mean of 70 and a standard deviation of 11.5. Find P81, which separates the bottom 81% from the top 19%. B) 73.3 C) 80.1 18) 19) D) 0.291 20) Scores on an English test are normally distributed with a mean of 37.6 and a standard deviation of 7.6. Find the score that separates the top 59% from the bottom 41% A) 35.9 B) 33.1 C) 42.1 D) 39.3 3 17) D) 102.6 18) Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Find the probability that a randomly selected adult has an IQ between 90 and 120 (somewhere in the range of normal to bright normal). A) 0.6014 B) 0.6227 C) 0.6568 D) 0.6977 A) 0.88 16) 20) 21) Human body temperatures are normally distributed with a mean of 98.20F and a standard deviation of 0.62F. Find the temperature that separates the top 7% from the bottom 93%. Round to the nearest hundredth of a degree. A) 98.40F B) 98.78F C) 99.12F D) 97.28F Assume that X has a normal distribution, and find the indicated probability. 22) The mean is = 15.2 and the standard deviation is = 0.9. Find the probability that X is greater than 16.1. A) 0.8413 B) 0.1550 C) 0.1587 23) The mean is = 137.0 and the standard deviation is = 5.3. Find the probability that X is between 134.4 and 140.1. A) 0.8138 B) 1.0311 C) 0.6242 21) 22) D) 0.1357 23) D) 0.4069 Find the indicated probability. 24) 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) 97.72% C) 37.45% D) 2.28% 24) Express the confidence interval using the indicated format. ^ 25) Express the confidence interval (0.668, 0.822) in the form of p E. A) 0.668 0.077 B) 0.745 0.077 C) 0.745 0.154 25) D) 0.668 0.154 Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 26) n = 125, x = 72; 90% confidence 26) A) 0.502 < p < 0.650 B) 0.503 < p < 0.649 C) 0.507 < p < 0.645 D) 0.506 < p < 0.646 Use the given data to find the minimum sample size required to estimate the population proportion. ^ ^ 27) Margin of error: 0.024; confidence level: 95%; p and q unknown A) 1668 B) 1776 C) 1492 27) D) 669 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. 28) Test scores: n = 75, x = 46.1, = 5.8; 98% confidence 28) A) 44.8 < < 47.4 B) 44.5 < < 47.7 C) 45.0 < < 47.2 D) 44.4 < < 47.8 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. 29) A sociologist develops a test to measure attitudes towards public transportation, and 27 29) randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects. A) 69.2 < < 83.2 B) 64.2 < < 88.2 C) 67.7 < < 84.7 D) 74.6 < < 77.8 4 Use the given information to find the minimum sample size required to estimate an unknown population mean . 30) How many business students must be randomly selected to estimate the mean monthly 30) earnings of business students at one college? We want 95% confidence that the sample mean is within $128 of the population mean, and the population standard deviation is known to be $ 536. A) 95 B) 68 C) 59 D) 47 5