# Mathematics

Draw a new gravitational potential energy vs. height graph to represent the gravitational potential energy if the ball had a mass of 2.00 kg. The graph for a 1.00-kg ball with an *arbitrary* initial velocity is provided again as a reference.

Take *g*=10.0m/s2 as the acceleration due to gravity.A 1.00 kg ball is thrown directly upward with an initial speed of 16.0 m/s.

A graph of the ball’s gravitational potential energy vs. height, *U*g(*h*), for an *arbitrary*initial velocity is given in Part A. The zero point of gravitational potential energy is located at the height at which the ball leaves the thrower’s hand.

For this problem, take *g*=10.0m/s2 as the acceleration due to gravity.

Chapter 7 Test

Question 1 A sample of 35 different payroll departments found that employees worked an average of 240.6 days a year. If the population standard deviation is 18.8 days, find the 90% confidence interval for the average number of days worked by all employees who are paid through payroll departments. a. 234.8 < μ < 248.8 b. 230.9 < μ < 250.3 c. 235.4 < μ < 245.8 d. 236.8 < μ < 244.4

Question 2 A student looked up the number of years served by 35 of the more than 100 Supreme Court justices. The average number of years served by those 35 justices was 13.8. If the standard deviation of the entire population is 7.3 years, find the 95% confidence interval for the average number of years served by all Supreme Court justices? a. 11.4 < μ < 16.2 b. 11.8 < μ < 15.8 c. 12.2 < μ < 15.4 d. 12.6 < μ < 15.0

Question 3 An economics professor randomly selected 100 millionaires in the United States. The average age of these millionaires was 54.8 years. If the standard deviation of the entire population of millionaires is 7.9 years, find the 95% confidence interval for the mean age of all United States millionaires? a. 54.0 < μ < 55.6 b. 53.5 < μ < 56.1 c. 53.3 < μ < 56.3 d. 52.8 < μ < 56.8

Question 4 A study of 35 professors showed that the average time they spent creating test questions was 13.5 minutes per question. The standard deviation of the population is 3.8. Which of the following is the 99% confidence interval for the average number of minutes it takes to create a test question? a. 12.0 < μ < 15.0 b. 10.2 < μ < 16.8 c. 11.8 < μ < 15.2 d. 12.7 < μ < 14.3

Question 5 A study of 55 white mice showed that their average weight was 3.2 ounces. The standard deviation of the population is 0.9 ounces. Which of the following is the 90% confidence interval for the mean weight per white mouse? a. 3.00 < μ < 3.40 b. 3.04 < μ < 3.36 c. 3.10 < μ < 3.30 d. 2.80 < μ < 3.60

Question 6 If a population has a standard deviation of 18, what is the minimum number of samples that need to be averaged in order to be 95% confident that the average of the means is within 2 of the true mean? a. 612 b. 18 c. 312 d. 36

Question 7 A researcher conducted a study of the access speed of 35 hard drives and concluded that his maximum error of estimate was 35. If he were to conduct a second study to reduce the maximum error of estimate to 7, about how many hard drives should he include in his new sample? a. 35 b. 70 c.175 d.875

Question 8 A study of elephants is conducted to determine the average weight of a certain subspecies of elephants. The standard deviation for the population is 500 pounds. At a 80% level, how many elephants need to be weighed so the average weight will be accurate to within 300 pounds? a. 5 b. 6 c. 8 d. 25

Question 9 A food snack manufacturer samples 11 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 15.2 oz. and the sample standard deviation is 0.40 oz., find the 95% confidence interval of the true mean. a. 15.1 < μ < 15.3 b. 14.3 < μ < 16.1 c. 13.4 < μ < 17.0 d. 14.9 < μ < 15.5

Question 10 The winning team’s score in 13 high school basketball games was recorded. If the sample mean is 54.3 points and the sample standard deviation is 11.0 points, find the 98% confidence interval of the true mean. a. 51.2 < μ < 57.4 b. 46.1 < μ < 62.5 c 47.2 < μ < 61.4 d. 37.9 < μ < 70.7

Question 11 If p̂ is equal to 0.73, then q̂ is equal to ______. a. 0.73 b. 0.50 c. 0.33 d. 0.27

Question 12 A survey of 800 women shoppers found that 17% of them shop on impulse. What is the 98% confidence interval for the true proportion of women shoppers who shop on impulse? a. 0.167 < p < 0.173 b. 0.144 < p < 0.196 c. 0.139 < p < 0.201 d. 0.136 < p < 0.204

Question 13 A random sample of 100 voters found that 44% were going to vote for a certain candidate. Find the 99% limit for the population proportion of voters who will vote for that candidate. a. 11.2% < p < 56.8% b. 32.7% < p < 55.3% c. 34.3% < p < 53.7 % d. 37.7% < p < 50.4%

Question 14 A random sample of 70 printers discovered that 20 of them were being used in small businesses . Find the 99% limit for the population proportion of printers that are used in small businesses. a. 0.021 < p < 0.551 b. 0.146 < p < 0.425 c. 0.160 < p < 0.412 d. 0.239 < p < 0.332

Question In a sample of 55 mice, a biologist found that 42% were able to run a maze in 30 seconds or less. Find the 90% limit for the population proportion of mice who can run a maze in 30 seconds or less. a. 36.5% < p < 47.5% b. 33.5% < p < 50.5% c. 31.0% < p < 53.0% d. 25.5% < p < 58.5%

Question 16 It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets. What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets? a. 0.620 < p < 0.780 b. 0.591 < p < 0.812 c. 0.584 < p < 0.830 d. 0.615 < p < 0.805

Question 17 The Pizza Shop wanted to determine what proportion of its customers ordered only cheese pizza. Out of 80 customers surveyed, 15 ordered only cheese pizza. What is the 99% confidence interval of the true proportion of customers who order only cheese pizza? a. 0.075 < p < 0.300 b . 0.086 < p < 0.289 c. 0.102 < p < 0.273 d. 0.115 < p < 0.260

Question 18 A recent poll of 700 people who work indoors found that 278 smoke. If the researchers want to be 98% confident of their results to within 3.5 percentage points, how large a sample is necessary? a. 751 b. 1062 c. 33 d. 532

Question 19 A report states that 46% of home owners have a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 4 percentage points with 92% confidence? a. 140 b. 238 c. 309 d. 476

Question 20 The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this proportion is within 3 percentage points of the true proportion. How large a sample is necessary? a. 966 b. 683 c. 1183 d. 484

Question 21 What is the value for χ left 2 for a 95% confidence interval when n =

18? a. 7.564 b. 8.672 c. 9.390 d. 8.231

Question 22 What is the value for χright 2 for a 98% confidence interval when

n=12 ? a. 27.688 b. 24.725 c. 21.920 d. 26.217

Question 23 What is the 95% confidence interval for the standard deviation of birth weights at County General Hospital, if the standard deviation of the last 25 babies born there was 1.1 pounds? a. 0 < σ < 2.1 b. 0 .7< σ < 2.3 c. 0.8 < σ < 1.9 d. 0.9 < σ < 1.5

Question 24 For a random sample of 23 European countries, the variance on life expectancy was 7.3 years. What is the 95% confidence interval for the variance of life expectancy in all of Europe? a. 27.2 < σ2 < 118.3 b. 5.6 < σ2 < 10.3 c. 4.4 < σ2 < 14.6 d. 28.9 < σ2 < 115.0

Question 25 Find the 95% confidence interval for the variance of the heights of maple trees if a sample of 26 trees has a standard deviation of 10.2 feet. a. 6.2 < σ2 < 14.2 b. 8.0 < σ2 < 14.1 c. 78.0 < σ2 < 130.0 d. 64.0 < σ2 < 198.2