4) Compare the scores: a score of 88 on a test with a mean of 79 and a score of 78 on a test with a mean of 70.

Transcription

1 Problem Set 3 Name MULTIPLE CHOICE. Please show all your work in the space provided or on scratch paper. Problems on scratch paper must be numbered and written legibly. Choose the one alternative that best completes the statement or answers the question. 1) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individualʹs IQ score is found to be 90. Find the -score corresponding to this value. A) B) C) 0.67 D) ) Find the probability of occurring in the indicated region. 2) 2) A) B) C) D) ) Compare the scores: a score of 75 on a test with a mean of 65 and a standard deviation of 8 and a score of 75 on a test with a mean of 70 and a standard deviation of 4. A) A score of 75 with a mean of 70 and a standard deviation of 4 is better. B) A score of 75 with a mean of 65 and a standard deviation of 8 is better. C) You cannot determine which score is better from the given information. D) The two scores are statistically the same. 3) 4) Compare the scores: a score of 88 on a test with a mean of 79 and a score of 78 on a test with a mean of 70. A) A score of 75 with a mean of 65 and a standard deviation of 8 is better. B) The two scores are statistically the same. C) You cannot determine which score is better from the given information. D) A score of 75 with a mean of 70 and a standard deviation of 4 is better. 4) 5) The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. Find the probability of a pregnancy lasting more than 300 days. A) B) C) D) ) 1

2 6) Find the -score that is greater than the mean and for which 70% of the distributionʹs area lies to its left. A) 0.81 B) 0.98 C) 0.53 D) ) 7) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individualʹs IQ score is found to be 110. Find the -score corresponding to this value. A) 1.33 B) C) D) ) Find the probability of occurring in the indicated region. 8) 8) A) B) C) D) ) Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 75 women are randomly selected, find the probability that they have a mean height between 63 and 65 inches. A) B) C) D) ) 10) The distribution of cholesterol levels in teenage boys is approximately normal with μ = 170 and σ = 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention. Find the probability that a teenage boy has a cholesterol level greater than 225. A) B) C) D) ) 11) Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 100 women are randomly selected, find the probability that they have a mean height greater than 63.0 inches. A) B) C) D) ) 12) Assume that blood pressure readings are normally distributed with a mean of 125 and a standard deviation of 4.8. If 36 people are randomly selected, find the probability that their mean blood pressure will be less than 127. A) B) C) D) ) 2

3 13) Find the area of the indicated region under the standard normal curve. 13) A) B) C) D) ) Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $32,000 and a standard deviation of $3000. If a teacher is selected at random, find the probability that he or she makes more than $36,000. A) B) C) D) ) 15) Two high school students took equivalent language tests, one in German and one in French. The student taking the German test, for which the mean was 66 and the standard deviation was 8, scored an 82, while the student taking the French test, for which the mean was 27 and the standard deviation was 5, scored a 35. Compare the scores. A) A score of 82 with a mean of 66 and a standard deviation of 8 is better. B) The two scores are statistically the same. C) You cannot determine which score is better from the given information. D) A score of 35 with a mean of 27 and a standard deviation of 5 is better. 15) 16) Compare the scores: a score of 220 on a test with a mean of 200 and a standard deviation of 21 and a score of 90 on a test with a mean of 80 and a standard deviation of 8. A) You cannot determine which score is better from the given information. B) The two scores are statistically the same. C) A score of 220 with a mean of 200 and a standard deviation of 21 is better. D) A score of 90 with a mean of 80 and a standard deviation of 8 is better. 16) 17) SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests while a junior and scores 860 on the SAT and 16 on the ACT. Compare the scores. A) A score of 16 on the ACT test was better. B) The two scores are statistically the same. C) A score of 860 on the SAT test was better. D) You cannot determine which score is better from the given information. 17) 18) Use the standard normal distribution to find P(-2.50 < < 1.50). A) B) C) D) ) 19) Use the standard normal distribution to find P(-2.25 < < 1.25). A) B) C) D) ) 20) Find the area under the standard normal curve to the right of = A) B) C) D) ) 3

4 Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution. 21) The monthly rents for studio apartments in a certain city have a mean of $1040 and a standard 21) deviation of $170. Random samples of sie 30 are drawn from the population and the mean of each sample is determined. A) $189.88, $31.04 B) $1040, $5.67 C) $189.88, $170 D) $1040, $ ) Assume that blood pressure readings are normally distributed with a mean of 120 and a standard deviation of 8. If 100 people are randomly selected, find the probability that their mean blood pressure will be greater than 122. A) B) C) D) ) 23) An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability that during a given week the airline will lose between 10 and 20 suitcases? A) B) C) D) ) 24) Ten percent of the population is left-handed. In a class of 100 students, write the binomial probability for the statement ʺThere are exactly 12 left-handed students in the class.ʺ A) P(x = 12) B) P(x 12) C) P(x > 12) D) P(x 12) 24) 25) Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. If 64 men are randomly selected, find the probability that they have a mean height between 68 and 70 inches. A) B) C) D) ) 26) A survey of 400 non-fatal accidents showed that 189 involved the use of a cell phone. Find a point estimate for p, the population proportion of non-fatal accidents that involved the use of a cell phone. A) B) C) D) ) 27) Find the value of E, the margin of error, for c = 0.90, n = 16 and s = 2.5. A) 0.84 B) 0.21 C) 0.27 D) ) 28) In a random sample of 28 families, the average weekly food expense was $95.60 with a standard deviation of $ Determine whether a normal distribution or a t -distribution should be used or whether neither of these can be used to construct a confidence interval. Assume the distribution of weekly food expenses is normally shaped. A) Use the t-distribution. B) Cannot use normal distribution or t-distribution. C) Use normal distribution. 28) 29) A researcher wishes to estimate the number of households with two cars. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 5%? A previous study indicates that the proportion of households with two cars is 19%. A) 413 B) 8 C) 237 D) ) 4

5 30) A random sample of 15 statistics textbooks has a mean price of $105 with a standard deviation of $ Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval. Assume the distribution of statistics textbook prices is not normally distributed. A) Use the t-distribution. B) Cannot use normal distribution or t-distribution. C) Use normal distribution. 30) 31) Find the value of E, the margin of error, for c = 0.99, n = 10 and s = 3.2. A) 3.29 B) 3.21 C) 1.04 D) ) 32) In order to efficiently bid on a contract, a contractor wants to be 95% confident that his error is less than two hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the standard deviation is 4.5 hours. How large a sample must be selected? A) 19 B) 4 C) 5 D) 20 32) Assume the sample is taken from a normally distributed population and construct the indicated confidence interval. 33) The dotplot shows the weights (in pounds) of 15 dogs selected randomly from those adopted out 33) by an animal shelter last week. Construct a 98% confidence interval for the population variance. Weights Pounds A) (1.74, 4.36) B) (3.03, 18.97) C) (2.89, 16.91) D) (3.38, 15.70) 34) A group of 49 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8. Construct a 98% confidence interval for the population mean. A) (18.8, 26.3) B) (20.3, 24.5) C) (21.1, 23.7) D) (19.8, 25.1) 34) 35) Construct a 90% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 15 randomly selected students has a grade point average of 2.86 with a standard deviation of A) (2.37, 3.56) B) (2.41, 3.42) C) (2.28, 3.66) D) (2.51, 3.21) 35) 36) A random sample of 150 students has a grade point average with a standard deviation of Find the margin of error if c = A) 0.15 B) 0.12 C) 0.11 D) ) 37) A random sample of 150 students has a grade point average with a mean of 2.86 and with a standard deviation of Construct the confidence interval for the population mean, μ, if c = A) (2.71, 3.01) B) (2.51, 3.53) C) (2.31, 3.88) D) (2.43, 3.79) 37) 5

6 38) Scores on a test have a mean of 72 and a standard deviation of 12. Random samples of sie 64 are drawn from this population and the mean of each sample is determined. Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution. 38) A) 9, B) 72, C) 72, D) 72, ) What happens to the mean and standard deviation of the distribution of sample means as the sie of the sample decreases? A) The mean of the sample means stays constant and the standard error increases. B) The mean of the sample means stays constant and the standard error decreases. C) The mean of the sample means increases and the standard error stays constant. D) The mean of the sample means decreases and the standard error increases. 39) 6

7 40) Assume that blood pressure readings are normally distributed with μ= 120 and σ = 8. A blood pressure reading of 145 or more may require medical attention. What percent of people have a blood pressure reading greater than 145? A) 6.06% B) 0.09% C) 99.91% D) 11.09% 40) 41) Find the probability that in 200 tosses of a fair six-sided die, a five will be obtained at most 40 times. A) B) C) D) ) 42) Find the area of the indicated region under the standard normal curve. 42) A) B) C) D) ) An airline reports that it has been experiencing a 15% rate of no-shows on advanced reservations. Among 150 advanced reservations, find the probability that there will be fewer than 20 no -shows. A) B) C) D) ) 44) A survey of 2450 golfers showed that 281 of them are left-handed. Construct a 98% confidence interval for the proportion of golfers that are left-handed. A) (0.203, 0.293) B) (0.683, 0.712) C) (0.369, 0.451) D) (0.100, 0.130) 44) 45) A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 99% confident that the true mean is within 2 ounces of the sample mean? The standard deviation of the birth weights is known to be 7 ounces. A) 9 B) 81 C) 10 D) 82 45) Assume the sample is taken from a normally distributed population and construct the indicated confidence interval. 46) The stem-and-leaf plot shows the test scores of 16 randomly selected students. Construct a 99% 46) confidence interval for the population standard deviation A) (7.89, 19.07) B) (7.61, 20.33) C) (62.18, ) D) (57.97, ) 47) A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of 48,400 miles and a standard deviation of 5000 miles. If the manufacturer is willing to replace no more than 10% of the tires, what should be the approximate number of miles for a warranty? A) 42,000 B) 54,800 C) 56,625 D) 40,175 47) 7

8 48) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the IQ score that corresponds to a -score of A) B) C) D) ) 49) Construct a 90% confidence interval for the population mean, μ. Assume the population has a normal distribution. In a recent study of 22 eighth graders, the mean number of hours per week that they watched television was 19.6 with a standard deviation of 5.8 hours. A) (19.62, 23.12) B) (18.63, 20.89) C) (5.87, 7.98) D) (17.47, 21.73) 49) 50) SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests while a junior and scores 1130 on the SAT and 25 on the ACT. Compare the scores. A) The two scores are statistically the same. B) You cannot determine which score is better from the given information. C) A score of 25 on the ACT test was better. D) A score of 1130 on the SAT test was better. 50) 8