Chapter 4-6 Test

Roll one 8-sides die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is given by

(10 3)*(1/8)^3*(7/8)^7

You draw two marbles at random from a jar that has 20 red marbles and 30 black marbles without replacement. What is the probability that both marbles are red?

0.1551

You select one musician from this group at random. What is the probability that this person plays a woodwind?

0.159

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume the X is Normal with mean $360 and standard deviation $50. What is P(X>$400)?

0.2119

A random variable X has a probability distribution as follows: X 0 1 2 3 P(x) 2k 3k 13k 2k Where k is a positive constant. The probability P(X<2.0) is equal to

0.25

A marketing survey compiled data on the total number of televisions in households. If X= the number of televisions in a randomly-selected household, and we omit the rare cases of more than 5 televisions, then X has the following distribution

0.39

Dwayne has collected data on the number of occupants of cars travelling on the road past his house for the past week. Based on his data, he has constructed a probability model for the number of occupants of a randomly-selected car on his street. Which of the following could be his model?

1 - 0.5, 2 - 0.25, 3 - 0.1, 4 - 0.15, >5 - 0.4

A business evaluates a proposed venture as follows. It stands to make a profit of $10,000 with probability 3/20, to make a profit of $5000 with probability 9/20, to break even with probability 5/20, and to lose $5000 with probability 3/20. The expected profit in dollars is

3000

A fair coin is tossed for times, and each time the coin lands heads up. If the coin is then tossed 1996 more times, how many heads are most likely to appear in these 1996 additional tosses?

998

A survey was done in the town of Mechanicsville to estimate the proportion of cars that are red and made by companies based in Japan. A simple random sample of 25 cars from a parking lot at Lee Davis High School was taken. Which of the following statements is correct?

A different team doing the sampling independently would probably obtain a slightly different answer for their sample proportion

Which of the following is a true statement?

An important difference between binomial and geometric random variables is that there is a fixed number of trials in a binomial setting, and the number of trials varies in a geometric setting.

Control groups are used in experiments to accomplish which one of the following?

Limit the effects of variables other than the explanatory variable on the outcome

Jen's commute to work requires that she take the Blue subway line, then transfer to the Red line. The length of the trip on the Blue line has a mean of 18 minutes with a standard deviation of 2 minutes. The Red line trip takes 12 minutes with a standard deviation of 1 minute. The waiting time between when she gets off the Blue line and her Red line train arrives has mean of 10 minutes and a standard deviation of 5 minutes. Assume that these items are independent random variables. What are the mean and standard deviation of her entire commute?

Mean = 40 minutes; Standard deviation =5.48 minutes

In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the mean and standard deviation of the number of students in the sample who have experienced math anxiety is

Mu (mean) = 2; standard deviation = 1.265

A researcher observes that, on average, the number of divorces in cities with Major Leagues Baseball team is larger than in cities without Major League Baseball teams. Which of the following is the most plausible explanation for this observed association?

The association is due to confounding

You select one musician from this group at random. Which o the following statement is true about the events "Plays woodwind" and "Male"?

The events are not mutually exclusive, nor are they independent

X and Y are independent random variables, and a and b are constants. Which one of the following statements is true?

Var(X-Y) = Var(X) + Var(Y)

A survey is to be administered to recent graduates of a certain nursing school in order to compare the starting salaries of women and men. For a random sample of graduates, three variables are to be recorded: sex, starting salary, and are of specialization. Which of the following best describes a conclusion that can be drawn from this study?

Whether there is an association between sex and starting salary among graduates for this nursing school.

You select 40 cards from a standard deck of 52 cards. Let Y be the number of red cards (hearts or diamonds) in the 40 cards selected. Which of the following best describes this setting?

Y has a binomial distribution with n = 40 observations and probability of success p = 0.5, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected.

To test the effect of music on productivity, a group of assembly line workers are given portable mp3 players to play whatever music they choose while working for one month. For another month, they work without music. The order of the two treatments for each worker is determined randomly. This is

a matched pairs experiment

A nutritionist wants to study the effect of storage time (6, 12, and 18 months) on the amount of vitamin C present in freeze dried fruit when stored for these lengths of time. Six fruit packs were randomly assigned to each of the three storage times. The treatment, experiment unit, and response are respectively:

a specific storage time, a fruit pack, amount of vitamin C

A maple sugar manufacturer wants to estimate the average trunk diameter of Sugar Maple trees in a large forest. There are too many to list them all and take a SRS, so he divides the forest into several hundred 10 meter by 10 meter plots, selects 25 plots at random, and measures the diameter of every Sugar Maple in each one. This is an example of a

cluster sample

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. We may conclude that

either A or B always occur

We wish to draw a sample of 5 without replacement from a population of 50 households. Suppose the households are numbered 01, 02, ..., 50, and suppose that the relevant line of the random number table is 11362 35692 96237 90842 46843 62719 64049 17823.

households 11 36 23 08 42

A new headache remedy was given to a group of 35 subjects who had headaches. Four hours after taking the new remedy, 20 of the subjects reported that their headaches had disappeared. From this information you conclude

nothing, because there is no control group for comparison

A researcher for a consumer products company is field testing a new formula for laundry detergent. He has contracted with 60 families, each with 2 children, who have agreed to test the product. He randomly assigns 30 families to the group that will use the new formula and 30 to the group that will use the company's current detergent formula. The most important reason for this random assignment is that

randomization is a good way to create two groups of 30 families that are as similar as possible, so that comparisons can be made between the two groups