Problems to look over Ch7-8 Name 1) Find the area of the indicated region under the standard normal curve. 1) A) 0.4032 B) 0.0823 C) 0.0968 D) 0.9032 2) Find the area under the standard normal curve between z = 0 and z = 3. Answer: B 2) A) 0.0010 B) 0.4987 C) 0.4641 D) 0.9987 3) Find the sum of the areas under the standard normal curve to the left of z = -1.25 and to the right of 3) z = 1.25. A) 0.7888 B) 0.1056 C) 0.2112 D) 0.3944 Find the probability of z occurring in the indicated region. 4) 4) 0 1.75 A) 0.0228 B) 0.0668 C) 0.9599 D) 0.0401 5) Use the standard normal distribution to find P(0 < z < 2.25). 5) A) 0.7888 B) 0.5122 C) 0.4878 D) 0.8817 1
6) Use the standard normal distribution to find P(z < -2.33 or z > 2.33). Answer: B 6) A) 0.0606 B) 0.0198 C) 0.7888 D) 0.9802 Use the Standard Normal Table to find the probability. 7) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An 7) individual's IQ score is found to be 110. Find the z-score corresponding to this value. Answer: B A) -0.67 B) 0.67 C) 1.33 D) -1.33 8) The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a 8) standard deviation of 15 days. Find the probability of a pregnancy lasting more than 300 days. A) 0.2375 B) 0.3189 C) 0.9834 D) 0.0164 9) An airline knows from experience that the distribution of the number of suitcases that get lost each 9) week on a certain route is approximately normal with µ = 15.5 and = 3.6. What is the probability that during a given week the airline will lose less than 20 suitcases? Answer: A A) 0.8944 B) 0.4040 C) 0.3944 D) 0.1056 10) Assume that the heights of women are normally distributed with a mean of 63.6 inches and 10) a standard deviation of 2.5 inches. The U.S. Army requires that the heights of women be between 58 and 80 inches. If a woman is randomly selected, what is the probability that her height is between 58 and 80 inches? P(58<x<80) = 0.9875 11) The distribution of cholesterol levels in teenage boys is approximately normal with µ = 170 11) and = 30. Levels above 200 warrant attention. If 95 teenage boys are examined, how many would you expect to have cholesterol levels greater than 225? normalcdf( 225, E99, 170, 30) = 0.0334 0.0334 (95) = 3.173 About 3 teenage boys 12) Find the z-score for the value 55, when the mean is 58 and the standard deviation is 3. 12) A) z = 0.90 B) z = -1.33 C) z = -1.00 D) z = -0.90 13) A student's score on the SAT-1 placement test for U.S. history is in the 90th percentile. 13) What can you conclude about the student's test score? The students test score was higher than the scores of 90% of the students who took the test. 2
14) Find the z-score that corresponds to the given area under the standard normal curve. 14) z = -0.58 15) Find the z-score that corresponds to the given area under the standard normal curve. 15) z = 3.07 16) Find the z-scores for which 90% of the distribution's area lies between -z and z. Answer: A 16) A) (-1.645, 1.645) B) (-2.33, 2.33) C) (-0.99, 0.99) D) (-1.96, 1.96) 17) For the standard normal curve, find the z-score that corresponds to the 30th percentile. Answer: A 17) A) -0.53 B) -0.12 C) -0.98 D) -0.47 18) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the 18) x-score that corresponds to a z-score of 2.33. Answer: A A) 134.95 B) 142.35 C) 139.55 D) 125.95 19) The lengths of pregnancies are normally distributed with a mean of 273 days and a standard 19) deviation of 20 days. If 64 women are randomly selected, find the probability that they have a mean pregnancy between 273 days and 275 days. A) 0.2119 B) 0.5517 C) 0.2881 D) 0.7881 Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution. 20) The amounts of time employees of a telecommunications company have worked for the company 20) are normally distributed with a mean of 5.1 years and a standard deviation of 2.0 years. Random samples of size 18 are drawn from the population find the mean and standard deviation of the mean of each sample. A) 5.1 years, 0.11 years B) 1.2 years, 0.47 years C) 5.1 years, 0.47 years D) 1.2 years, 2.0 years 3
21) In a recent survey, 80% of the community favored building a police substation in their 21) neighborhood. You randomly select 23 citizens and ask each if he or she thinks the community needs a police substation. Decide whether you can use the normal distribution to approximate the binomial distribution. If so, find the mean and standard deviation. If not, explain why. Cannot use the normal to approximate the binomial because nq = (23)(0.2) = 4.6 < 5 22) Ten percent of the population is left-handed. A class of 100 students is selected. Convert the 22) binomial probability P(x < 12) to a normal probability by using the correction for continuity. Answer: B 12 is a right endpoint A) P(x > 12.5) B) P(x 12.5) C) P(x < 11.5) D) P(x 11.5) 23) The failure rate in a statistics class is 20%. In a class of 30 students, find the probability that 23) exactly five students will fail. Use the normal distribution to approximate the binomial distribution. P(r = 5) = P(4.5 < x < 5.5) = P( -0.68 < z < -0.23) = 0.1630 24) A random sample of 40 students has a mean annual earnings of $3120 and a standard deviation of 24) $677. Find the margin of error if c = 0.95. Answer: A use tc A) $217.3 B) $2891 C) $7 D) $77 25) A random sample of 120 students has a test score average with a standard deviation of 9.2. Find the 25) margin of error if c = 0.98. Answer: B use tc A) 0.18 B) 1.985 C) 0.82 D) 0.84 26) Find the critical value zc that corresponds to a 95% confidence level. 26) A) ±1.645 B) ±2.575 C) ±1.96 D) ±2.33 27) A random sample of 150 students has a grade point average with a mean of 2.86 and with a 27) standard deviation of 0.78. Construct the confidence interval for the population mean, µ, if c = 0.98. Answer: B use tc A) (2.31, 3.88) B) (2.71, 3.01) C) (2.43, 3.79) D) (2.51, 3.53) 28) A random sample of 40 students has a mean annual earnings of $3120 and a standard deviation of 28) $677. Construct the confidence interval for the population mean, µ if c = 0.95. Answer: B use tc A) ($1987, $2346) B) ($2903, $3337) C) ($4812, $5342) D) ($210, $110) 4
29) A group of 40 bowlers showed that their average score was 192 with a standard deviation of 8. Find 29) the 95% confidence interval of the mean score of all bowlers. Answer: B A) (188.5, 195.6) B) (189.4, 194.6) C) (186.5, 197.5) D) (187.3, 196.1) 30) In a random sample of 60 computers, the mean repair cost was $150 with a standard 30) deviation of $36. a) Construct the 99% confidence interval for the population mean repair cost. We are 99% confident that the mean repair cost of the computers is between $138 and $162, on average. b) If the level of confidence was lowered to 95%, what will be the effect on the confidence interval? A decrease in the confidence level will decrease the width of the confidence intercal. Lower confidence level narrower confidence interval. Higher confidence level wider confidence interval. 31) The number of wins in a season for 32 randomly selected professional football teams are 31) listed below. Construct a 90% confidence interval for the true mean number of wins in a season. 9 9 9 8 10 9 7 2 11 10 6 4 11 9 8 8 12 10 7 5 12 6 4 3 12 9 9 7 10 7 7 5 We are 95% confidence that the mean number of wins in a season is between 7.2 and 8.8, on average 32) The standard IQ test has a mean of 101 and a standard deviation of 16. We want to be 98% certain 32) that we are within 4 IQ points of the true mean. Determine the required sample size. A) 10 B) 1 C) 188 D) 87 33) In order to efficiently bid on a contract, a contractor wants to be 95% confident that his error is less 33) 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? Answer: B A) 5 B) 20 C) 4 D) 19 5
34) In order to set rates, an insurance company is trying to estimate the number of sick days that full 34) time workers at an auto repair shop take per year. A previous study indicated that the standard deviation was 2.8 days. How large a sample must be selected if the company wants to be 95% confident that the true mean differs from the sample mean by no more than 1 day? A) 1024 B) 512 C) 31 D) 141 35) Given the same sample statistics, which level of confidence will produce the narrowest 35) confidence interval: 75%, 85%, 90%, or 95%? Explain your reasoning. The 75% level of confidence will produce the narrowest confidence interval. As the level of confidence decreases the width of the interval becomes narrower. 36) Find the critical value, tc for c = 0.99 and n = 10. Use table in Textbook on page 36) A) 2.262 B) 1.833 C) 3.169 D) 3.250 37) Find the value of E, the margin of error, for c = 0.90, n = 16 and s = 2.5. 37) A) 0.21 B) 0.84 C) 0.27 D) 1.1 38) When 435 college students were surveyed,120 said they own their car. Find a point estimate for p, 38) the population proportion of students who own their cars. A) 0.724 B) 0.216 C) 0.381 D) 0.276 39) A survey of 250 homeless persons showed that 17 were veterans. Find a point estimate p, for the 39) population proportion of homeless persons who are veterans. Answer: B A) 0.932 B) 0.068 C) 0.073 D) 0.064 40) The Federal Bureau of Labor Statistics surveyed 50,000 people and found the 40) unemployment rate to be 5.8%. The margin of error was 0.2%. Construct a confidence interval for the unemployment rate. M.E. = 0.2% = 0.002 phat = 0.058 qhat = 1-0.058 = 0.942 n = 50,000 phat - M.E. = 0.056 phat + M.E. = 0.06 The confidence interval is (0.056, 0.06) 41) A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence 41) interval for the proportion of homeless persons who are veterans. A) (0.176, 0.274) B) (0.167, 0.283) C) (0.184, 0.266) D) (0.161, 0.289) 6
42) A researcher at a major hospital wishes to estimate the proportion of the adult population of the 42) United States that has high blood pressure. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%? A) 423 B) 1201 C) 601 D) 13 43) A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. How 43) 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 2%? A previous study indicates that the proportion of left-handed golfers is 8%. A) 707 B) 17 C) 1086 D) 999 44) The mean IQ score of adults is 100, with a standard deviation of 15. Use the Empirical Rule to find 44) the percentage of adults with scores between 70 and 130. (Assume the data set has a bell-shaped distribution.) Answer: A A) 95% B) 68% C) 100% D) 99.7% 7