Algebra2 Name
Unit 7 Review part 2 of unitDateHour
1. Some sources say that the average height of men worldwide is 69 inches with standard deviation 2.8 inches. Suppose that the heights of men worldwide are almost normally distributed. Use the graphing calculator to answer these questions. Round percent answers to the nearest tenth of a percent and height answers to the nearest tenth of an inch. Shade/sketch the normal distribution to show how you organize your work. Each question will use either normalcdf(lower, upper, ) or invNorm(area, ).
a. Approximately what percent of men are between 65 and 70 inches tall?
b. Approximately what percent of men are taller than 70 inches?
c. Approximately what percent of men are shorter than 64 inches?
d. Approximately what height “cuts off” the shortest 40% of men?
e. Approximately what height “cuts off” the tallest 35% of men?
2. A student created a 6-sided die in his sculpture class. He rolled it 60 times and the table shows the results of these rolls. Does it appear that the die he made is a fair die? Explain.
Side of the die displayed / 1 / 2 / 3 / 4 / 5 / 6Number of rolls / 2 / 20 / 8 / 20 / 5 / 5
3. A certain candy comes in boxes that contain 3 colors. A box I bought recently contained 33 white, 34 pink, and 32 purple candies. The company claims that it manufactures the 3 colors in equal proportions. Does the box I bought seem consistent with this company’s claim? Explain.
4. A model says that on a certain spinner, the spinner stops on the blue section with probability 0.8. Suppose we spin the spinner 3 times and it stops on blue all 3 times.
a. What is the probability of this happening?
b. Would this result cause you to question the model? Explain.
5. A teacher gave a homework assignment to go home, find a coin, toss it 100 times, and come back the next day with the number of times that tails was displayed on the coin. The teacher suspects that her 56 students didn’t actually toss the coins, but rather, just made up some number of tails to report in class the next day. There are two distributions shown. “Penny” is the hypothetical distribution of number of tails that 56 students would get from 100 coin tosses each. “Classes” is the distribution of the number of tails that were reported by the teacher’s 56 students. Based on the graphs, does it seem like this teacher’s students really tossed their coins 100 times and reported the number of tails or just made up their numbers? Explain.
6. A teacher gave a homework assignment to go home, find a coin, toss it 100 times, and come back the next day with the number of times that tails was displayed on the coin. The teacher suspects that her 56 students didn’t actually toss the coins, but rather, just made up some number of tails to report in class the next day. There are two distributions shown. “Penny” is the hypothetical distribution of number of tails that 56 students would get from 100 coin tosses each. “Students” is the distribution of the number of tails that were reported by the teacher’s 56 students. Based on the graphs, does it seem like this teacher’s students really tossed their coins 100 times and reported the number of tails or just made up their numbers? Explain.
7. A student created a spinner that with 4 spaces that are supposed to be equally spaced. He gave it a spin it 80 times and the table shows the results of these spins. Does it appear that the spinner he made is a fair one? Explain.
Part the spinner stopped on / 1 / 2 / 3 / 4Number of spins / 19 / 20 / 21 / 20
8. My friend put together a bag of 25 marbles and claimed that 10 of the marbles are blue. Suppose that I reach into the bag without looking, draw out a marble, identify the color, and then replace it.
a. What is the probability of taking out a blue marble 2 times, replacing them each time?
b. If that would happen, would this result cause you to question the model? Explain.
c. What is the probability of taking out a blue marble 5 times, replacing them each time?
d. If that would happen, would this result cause you to question the model? Explain.
9. A student made a spinner with just 2 equal spaces (red or blue) on it and believes it is a fair spinner with a 50% chance of stopping on each space.
a. What is the probability of the spinner stopping on blue 3 times in a row?
b. If that would happen, would this result cause you to question the spinner’s fairness? Explain.
c. What is the probability of the spinner stopping on blue 7 times in a row?
d. If that would happen, would this result cause you to question the spinner’s fairness? Explain.
10. A board game uses a spinner and players win tokens according to the probabilities shown in the table below. If a player were to play this game many, many times, what is the expected number (average number) of tokens that the player would win from each spin?
1 token / 50%2 tokens / 30%
3 tokens / 10%
4 tokens / 10%
11. When a certain animal species has “pups”, the number of pups born have the distribution given in the table below. If we examine many, many births for this animal species, what is the average number (expected number) of pups?
1 pup / 20%2 pups / 40%
3 pups / 20%
4 pups / 10%
5 pups / 5%
6 pups / 5%
12. On a particular question on a test, there are 3 points possible for a student to earn. When the class took the test, the points earned followed the distribution given in the table. What was the average number of points earned on that question?
0 points / 20%1 point / 10%
2 points` / 30%
3 points / 40%
13. Two students took random samples from the same population and ended up with the same sample mean and same sample standard deviation. Student A had a sample of 40 items. Student B had a sample of 400 items. Was student A’s margin of error larger than student B’s, the same as student B’s, or smaller than student B’s? Explain.
14. Steve is a market researcher who took a random sample and his boss tells Steve that the resulting margin of error is too large to be of any use. Steve needs to take a sample that leads to a smaller margin of error. If we assume that the sample mean and sample standard deviation don’t change, what should Steve do next time—take a smaller sample, take the same size sample, or take a larger sample? Explain.
15. Bob took a random sample of 20 items and calculated the margin of error. If he increases his sample size to 50 items, and still has the same sample proportion, will his margin of error increase, stay the same, or decrease? Explain.
16. A chemist checked the pH (a common measure of how acidic something is) for a sample of 6 sources of a grape juice and the average for the sample was 3.225 and the margin of error was 0.305. Explain what the margin of error 0.305 means.
17. From a certain population, we take a sample of 18 items. If the smallest sample mean we would expect is 64 and the largest sample mean we would expect is 80, then what is the margin of error?
18. A consumer advocate estimates that the mean number of miles that a certain car will travel per mile of gasoline is between 20 miles and 28 miles. What is the margin of error that this consumer advocate used?
19. An inspector took a random sample of 120 products produced during one work shift. The inspector found that 20 of the 120 items had a minor scratch (17% had a minor scratch) and then calculated that the margin of error is 11%. Explain what the margin of error 11% means.
20. At a particular university, we asked a random sample of 200 students about the highest level of education their parents had achieved. Suppose that the smallest sample proportion we would expect to reply “Masters Degree” is 32% and the largest sample proportion we would expect to respond “Masters Degree” is 40%. What is the margin of error?
On questions 21 and 22, Use the correct margin of error formula:
for categorical data: or for quantitative data:
21. Bats aren’t known for good eyesight, so they use high-pitched sounds and locate prey by listening for echoes. Researchers measured the centimeters away that a sample of 11 bats could first detect a nearby insect (their main source of food). If 48.36 cm and s = 18.08 cm, what is the margin of error?
22. A shipment of printer cartridges has arrived from the manufacturer and a random sample of 200 cartridges is selected for inspection and testing. Suppose that 14 of them are found to have a defect. What is the margin of error?
On questions 23-28, Use the correct confidence interval formula:
for categorical data: or for quantitative data:
23. A consumer watchdog/advocate weighs a random sample of 45 of packages of snack mix from a company’s marketing area and finds a sample mean of 11.92 ounces and a standard deviation of 0.2 of an ounce. Construct and interpret a confidence interval to estimate the average weight for all packages of this brand.
24. A clothing manufacturer finds that a random sample of 500 women in a certain country have an average height of 66.5 inches and a standard deviation of 2.5 inches. The heights of these 500 women appear to be close to normally distributed. Construct and interpret a confidence interval to estimate the average height of women in that country.
25. A clothing manufacturer finds that a random sample of 200 men in a certain country have an average height of 68 inches and a standard deviation of 2.8 inches. The heights of these 200 men appear to be close to normally distributed. Construct and interpret a confidence interval to estimate the average height of men in that country.
26. An insurance company examined a random sample of 582 police records of traffic accidents and found that teenagers were driving in 91 of them. Construct and interpret a confidence interval to estimate the actual proportion of the traffic accidents involving teenage drivers.
27.A particular state has put an issue on the ballot for voters to decide whether to legalize a certain kind of gambling. One of the newspapers in the state’s largest city conducts a poll of 450 randomly selected voters from across the state and finds 243 people in favor of the proposal. Construct and interpret a confidence interval to estimate the actual proportion of all voters in the state who are in favor of legalizing this kind of gambling.
28.Wildlife biologist inspect 153 deer taken by hunters and find 32 of the deer carrying ticks that test positive for Lyme disease. Assume these 153 deer are a random sample of all deer in the region. Construct and interpreta confidence interval to estimate the actual proportion of all deer in the region that carry such ticks.