1. A normally distributed variable has a mean of 75 and a standard deviation of 2. What is the z-score for 81?(two marks) A L J B 3 2. What percent of values of a normally distributed variable lie between the mean and two standard deviations above the mean? (two marks) A 95% C 47.5% B 68% D 34% 3. A woodcarver produces walking sticks that follow a normal distribution with a mean length of 140 cm and a standard deviation of 12 cm. A stick is chosen at random from the day's production. Which length is least likely?(two marks)A 150 cm C 138 cm B 148 cm D 132 cm 4. The tag and release method was used to estimate the population of wolves in a provincial park. The findings were summarized as "the population is 217 wolves + 5%, 19 times out of 20." What is the margin of error? (three marks) A 19 out of 20 C the same as the standard deviation B +5% about 217 D 217 5. The tag and release method was used to estimate the population of wolves in a provincial park. The findings were summarized as "the population is 217 wolves + 5%, 19 times out of 20." If the study is repeated 20 times, how often would the researcher expect the mean number of wolves to be within 1 5% of 217?(four marks) A in at least 5% of the studies C in at least 95% of the studies B in at least 50% of the studies D in all of the studiesMatch the cement percent to each afthefottawirtg means. A percent may be used more than once or not at aft. A 34% l} 153% B 415% E 95% C 49.5% F 99% . The percent of data that are within one standard deviation of the mean. The fem of data that are between the mean and one standard deviation helovnr the mean. . The fem of data that are between the mean and two standard deviations above the mean. The fem of data that are within two standard deviations of the mean all. A confidence level D sample size B confidence interval E z-score C margin of error F repeated sampling 5. The smaller this is, the greater the accuracy of a measurement. 6. The probability that a particular statistic is within the range indicated by the margin of error. 7. The greater this is, the smaller the margin of error. 8. The range of possible values for the measured statistic at a particular confidence level. 9. Multiple samples of the same size taken from a population that follows a normal distribution.1. A magazine states a confidence level as 39 times out of 40. Express this as a percent. Is this a commonly used confidence level?(three marks)2. A 100 hp aircraft engine is expected to run a mean time of 2000 h before needing an overhaul, with a standard deviation of 100 h. The manufacturer tests random samples of 5 engines in each of the major markets where the engine is sold. What is the expected standard deviation of the sample means?(four marks) 3. A poll shows that the Social Party has 52% of the decided voters, while another poll shows that the Capital Party has 52% of the decided voters. Both claim an accuracy of 1 4%, 19 times out of 20. Can they both be accurate? Explain your answer.(four marks)4. A bakery produces cupcakes with a mean mass of 98 g and a standard deviation of 2 g. A cupcake is measured at random, and found to have a mass of 104 g. Should the baker be concerned? What should be done?(four marks) 5. The Berliner Jelly Donut Company claims that its donuts contain a mean of m grams of jelly. A sample of 100 donuts from the bakery line shows a mean of 78 g of jelly with a standard deviation of 12 g. What is a reasonable value for m at a confidence level of 95%?(five marks) 6. The average daily high in Port Forlorn in July is found to have a mean of 25 "C with a standard deviation of 5 "C. On how many days is the temperature expected to top 30 "C, assuming a normal distribution?(five marks)7. A newspaper survey reports that only 23% of the voters in a town favour construction of a new skateboard park. The survey claims an accuracy of 13.2%, 19 times out of 20. How many voters were surveyed? (five marks)
