AP Statistics: Unit 6 The mean maze

AP Statistics: Unit 6

Name: ___________________________________________

The mean maze

Directions: Solve each situation below. You MUST attach your work to this page. Once you solve, follow the path out of the maze. For example, on the START square, there are 3 possible answers. Whichever one you find, will lead you to the next question. The questions are located on the back of this page.

Start!

Question 2

Question 3

Question 4

Question 1 0.1501

47.5 in

0.5224

0.4470

Question 5

48.9 in

Question 6

.421

0.5904

0.77

Question 7

Question 8

.083

51.85 in

.356

.0568

.007

47.52 in

Question 9

Question 10

Question 11

Question 12

.357

.0027

.433

.9975

Question 13

.2378

Question 14

0.949

.000027

.00043

Question 15

Question 16

0.941

0.127

YES

NO

0.979

0.898

0.057

Question 17

Question 18

Question 19

0.0248

5.084

0.52

Question 1: The heights of mature pecan trees are approximately normally distributed with a mean of 42 feet and a standard deviation of 7.5 feet. What proportion of pecan trees are between 43 and 46 feet tall?

Question 2: Heights of fourth graders are normally distributed with a mean of 52 inches and a st deviation of 3.5 inches. Ten percent of fourth graders should have a height below what number?

Question 3: The distance Jalan can throw a shot put has a mean of 14.2 meters and a st deviation of 3.5 meters. Over the course of a month, Jalan makes 75 throws. What's the probability that his average shot put distance for the month will be over 15.0 meters?

Question 4: A company negotiator claims that only 35 percent of union members will support a strike, but a union representative believes the true percentage is greater and runs a hypothesis test at the 5 percent significance level. If 57 out of an SRS of 150 union members say they are willing to strike what is the test statistic?

Question 5: Fifty-three percent of adults say they have trouble sleeping. If a doctor contracts an SRS of 85 adults, what is the probability that over 55 percent will say they have trouble sleeping?

Question 6: The owner of a local Starbucks advertises that the price of coffee on any given day will be randomly picked using a normal distribution with a mean of $1.35 and standard deviation of $0.10. If a customer buys a cup of coffee every day for 10 days, what is the probability that he will pay a total exceeding $14.00?

Question 7: Suppose the average outstanding loan for college graduates is $23,500 with a standard deviation of $7,200. In an SRS of 50 graduating college students, what is the probability that their mean outstanding loan is under $21,000?

Question 8: Heights of 4th graders are approx. Normal with a mean of 52 in and a st deviation of 3.5 in. You plan to measure a SRS of 30 4th graders. 10% of the samples, like yours, should have an average height below what number?

Question 9: A new soft drink product has an average number of 77 calories per bottle with a standard deviation of 4.5 calories. In a random sample of 40 bottles, what is the probability that the mean number of calories is between 75 and 80 calories?

Question 10: It is known that 66 percent of the employees at one factory are women, while 57 percent of the employees of a second factory are women. In an SRS of 75 employees from the first factory and an independent SRS of 60 employees from the second, what is the probability that the difference between the percentages of women picked (first minus the second) is more than 15 percent?

Question 11: Enterprise manages car rentals and found that the tire lifetime for their vehicles has a mean of 50,000 mi and standard deviation of 3500 mi. What's the probability that the sample mean lifetime for these 50 vehicles exceeds 52,000?

Question 12: The company JCrew advertises that 95% of its online orders ship within two working days. You select a random sample of 200 of the 10,000 orders received over the past month to audit. The audit reveals that 180 of these orders shipped on time. If JCrew really ships 95% of its orders on time, what is probability that the proportion in a random sample of 200 orders is as small or smaller as the proportion in the audit?

Question 13: An office manager believes that the percentage of employees arriving late is even greater than the previously claimed 7 percent. She conducts a hypothesis test on a random 200 employees arrivals and finds 23 punching in late. Is this strong evidence against the 0.07 claim?

Question 14: In a random sample of 175 toddlers, 125 know what color the Cookie Monster is. If the margin of error in a given confidence interval is 0.079, what is the level of confidence?

Question 15: In a random survey of 450 adults, 28 percent said that they felt that their credit card debt is too high. With what degree of confidence can the pollster say that 28, give or take 4 percent, of adults believe that their credit card debt is too high?

Question 16: While visiting Maine, Andrew goes apple picking. An average weight of a gala apple is 80 grams with a standard deviation of 8 grams. Andrew fills a bag of 10 apples. What is the probability that the average of the apples will be below 75 grams?

Question 17: A survey was conducted to determine the number of protein shakes consumed by high school track athletes during a typical week. In a random sample of 1000 high school track athletes, 65 percent answered that they drank more than two protein shakes every week. Based on this sample, the margin of error for a 90 percent confidence interval for the proportion of high school track athletes who drink more than two protein shakes per week is...

Question 18: The diameter of a particular variety of oranges is normally distributed with a mean of 5 cm and a standard deviation of 0.5 cm. Suppose an orchard sells bags of 16 oranges, assuming that the bags are filled at random, 25 percent of the bags have a mean orange diameter greater than what?

Question 19: Golf balls must meet a certain standard of distance traveled in order to be used in a professional tournament. When the ball is hit by a mechanical device, under specific calibration, the ball may not travel farther than 291.2 yards in the air. From past data, a certain manufacturer has determined that the distances traveled for the balls it produces are normally distributed with a mean of 290 yards. What standard deviation, in yards, should the manufacturer require if they want 99% of balls they manufacture to meet the tournament standard?

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