Embedded Files
For problems 1) through 14) use the following information: On a particular stretch of road, the number of cars per hour produces a normal distribution with a mean of 125 cars per hour and a standard deviation of 40 cars per hour.
1) Sketch a normal curve for this situation. Be sure to label and mark the mean and 1 and 2 standard deviations above and below the mean.
2) What is the z-score for an observation of 165 cars in one hour?
3) What is the z-score for an observation of 85 cars in one hour?
4) Calculate the z-score associated with an observation of 171 cars in one hour.
5) Suppose 135 cars are observed in one hour. At what percentile would this observation occur?
6) Suppose 70 cars are observed in one hour. At what percentile would this observation occur?
7) At what percentile would an observation of 125 cars occur?
8) What is the probability of observing at least 145 cars on the road in a an hour?
9) What is the probability of observing between 100 and 150 cars on the road in an hour?
10) Determine the percentile for an observation of 140 cars on the road in one hour.
11) Determine the percentile for an observation of 65 cars on the road in one hour.
12) Determine the probability of observing between 90 and 130 cars on the road in one hour.
13) Determine the probability of observing at least 160 cars on the road in one hour.
14) Determine the probability of observing no more than 110 cars on the road in one hour.
For problems 15) through 20) use the following information: The number of ants found in one mature colony of leafcutter ants is normally distributed with a mean of 136 ants and a standard deviation of 14 ants.
15) One ant colony has 165 ants. At what percentile for size is this ant colony?
16) An ant colony has a z-score of -1.35 for size. How many ants would we expect to find in this colony?
17) Another ant colony has 131 ants. What is the z-score for this ant colony?
18) What is the probability of finding an ant colony with 160 ants or less?
19) What is the probability of finding an ant colony with 150 ants or more?
20) What is the probability of finding an ant colony that has between 120 and 155 ants in it?
21) Twin brothers Ricky and Robbie each took a college entrance exam. Ricky took the SAT which had a mean of 1000 with a Standard Deviation of 200 while Robbie took the ACT which had a mean of 18 with a standard deviation of 6. Which brother did better if Ricky scored a 1140 and Robbie scored a 22?
22) Suppose the average height of an adult American male is 69.5 inches with a standard deviation of 2.5 inches and the average height of an adult American female is 64.5 inches with a standard deviation of 2.3 inches. Who would be considered taller when compared to their gender, an adult American male who is 74 inches tall or an adult American female who is 68.5 inches tall? Explain your answer.
23) Professional golfer John Daly is one of the longest hitting golfers in history. Suppose his drives average 315 yards with a standard deviation of 12 yards. Will a drive of 345 yards be in his top 1% of his longest drives? Explain your answer.
Review Exercises
24) What is the area under any density curve equal to?
25) In a standard deck of 52 cards, what is the probability of being dealt two queens if you are dealt two cards from the deck without replacement?
26) In a class competition, each grade (9-12) enters 10 students to run in a 500 meter race. Boys times for 9th graders and 12th graders are given below in seconds. Build a back-to-back stem plot to compare data for the two groups of students.
9th Grade Times = 115, 118, 118, 121, 126, 127, 131, 134, 140
12th Grade Times = 106, 106, 109, 112, 114, 116, 116, 121, 122, 133
27) It turns out that countries that have higher percentages of people with computers also tend to have people who live longer. Is it logical to assume that shipping many computers to countries whose people have lower life-expectancies will help the people in those countries live longer? Answer the question including justification that references either Cause and Effect, Common Response, Confounding, or Coincidence.
28) A sample survey at a local college campus asked 250 students how many textbooks they were currently carrying. The table below shows a summary of the findings. Use the table to determine the expected number of textbooks that an average college student at this campus would be carrying.
Page updated
Report abuse