Discrete and Continuous Random Variables and Binomial Distribution Calculations

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The braking time of a car. Identify the given random variable as being discrete or continuous. A) Discrete B) Continuous 1) 2) Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n = 503; p = 0.7 A) σ = 13.55 B) σ = 10.28 C) σ = 7.87 D) σ = 14.40 2) 3) Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. n = 676; p = 0.7 A) μ = 474.5 B) μ = 474.9 C) μ = 473.2 D) μ = 471.7 3) 4) Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n = 38; p = 2/5 A) σ = 13.55 B) σ = 14.40 C) σ = 10.28 D) σ = 7.87 4) 5) Mars, Inc. claims that 20% of its M&M plain candies are orange. A sample of 100 such candies is randomly selected. Find the mean and standard deviation for the number of orange candies in such groups of 100. A) μ = 20, σ = 4.0 B) μ = .020, σ = .20 C) μ = 20, σ = .20 D) μ = .20, σ = 4.0 5) 6) The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. 6) x 1 2 3 4 5 6 P(x) 0.14 0.16 0.12 0.14 0.13 0.31 A) μ = 3.8 B) μ = 0.2 C) μ = 3.5 D) μ = 3.9 7) On a multiple choice test with 17 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers. A) 4.3 questions B) 8.5 questions C) 12.8 questions D) 5.7 questions 7) 8) A die is rolled nine 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 twos B) 2.25 twos C) 7.5 twos D) 1.5 twos 8) 9) In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest to ________. A) 669 adults B) 34 adults C) 344 adults D) 66 adults 9) 10) Assume that a procedure yields a binomial distribution with a trial repeated n = 30 times. Use the binomial probability formula to find the probability of x = 5 successes given the probability p = 1/5 of success on a single trial. Round to three decimal places. A) 0.067 B) 0.198 C) 0.172 D) 0.421 10) 11) A die is rolled nine 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) 7.5 twos B) 3 twos C) 1.5 twos D) 2.25 twos 11) 12) According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16. A) 2.8 students B) 0.2 students C) 3.5 students D) 4.0 students 12) 13) Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Rolling a single die 53 times, keeping track of the "fives" rolled. A) Not binomial: there are more than two outcomes for each trial. B) The procedure results in a binomial distribution. C) Not binomial: there are too many trials. D) Not binomial: the trials are not independent. 13) 14) A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 successful first serves in? Assume that each serve is independent of the others. A) 0.154 B) 0.00184 C) 0.0635 D) 0.133 14) 15) A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? Round to three decimal places. A) 0.828 B) 0.205 C) 0.377 D) 0.172 15) 16) The following table describes the results of roadworthiness tests of Ford Focus cars that are three years old (based on data from the Department of Transportation). The random variable x represents the number of cars that failed among six that were tested for roadworthiness: x 0 1 2 3 4 5 6 16) P(x) 0.377 0.399 0.176 0.041 0.005 0+ 0+ Find the probability of getting three or more cars that fail among six cars tested. A) 0.046 B) 0.005 C) 0.222 D) 0.048 17) 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 200 and 275. A) 0.9332 B) 0.4332 C) 0.0668 D) 0.5 17) 18) If z is a standard normal variable, find P(z > 0.97). A) 0.1922 B) 0.8340 18) C) 0.1660 D) 0.1685 19) In a population of 210 women, the heights of the women are normally distributed with a mean of 64.4 inches and a standard deviation of 2.9 inches. If 36 women are selected at random, find the mean μ and standard deviation σ of the population of sample means. Assume that the x x sampling is done without replacement and use a finite population correction factor. A) 64.4 inches, 0.44 inches B) 64.4 inches, 2.07 inches C) 58.8 inches, 2.65 inches D) 64.4 inches, 2.9 inches 19) 20) Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7. Find P81, which separates the bottom 81% from the top 19%. 20) A) 73.5 B) 0.88 C) 66.6 21) If z is a standard normal variable, find the probability: P(-0.73 < z < 2.27) A) 0.7557 B) 0.2211 C) 1.54 D) 0.291 21) D) 0.4884 22) 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 14 tosses. What is the probability of being correct 14 or more times by guessing? Does this probability seem to verify her claim? Use the normal distribution to approximate the desired probability. A) 0.4418, no B) 0.0582, no C) 0.4418, yes D) 0.0582, yes 22) 23) The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find the probability that he weighs between 170 and 220 pounds. A) 0.1554 B) 0.3811 C) 0.0703 D) 0.2257 23) 24) Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.4483. A) 0.6736 B) 0.13 C) -0.13 D) 0.3264 25) Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. A) 0.9656 B) 0.4656 C) 0.0344 24) 25) D) -0.0344 26) Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per microliter. Find the value closest to the probability that a randomly selected woman has a red blood cell count above the normal range of 4.2 to 5.4 million cells per microliter. A) 0.0158 B) 0.0409 C) 0.1611 D) 0.9842 26) 27) An unbiased estimator is a statistic that targets the value of the of the population parameter such that the sampling distribution of the statistic has a ________ equal to the ________ of the corresponding parameter. A) mean; standard deviation B) standard deviation; standard deviation C) mean; mean D) range; range/4 27)