Bus Stats Module 4

In one of its Spring catalogs, L.L. Bean® advertised footwear on 29 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested in the number of pages that advertise footwear. Each page may be picked at most once. How many pages do you expect to adversise footwear on them?

3.03

During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. DeAndre scored with 61.3% of his shots. Suppose you choose a random sample of 80 shots made by DeAndre during the 2013 season. Let X = the number of shots that scored points. What is the standard deviation of X? Fill input:

4.36

During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. DeAndre scored with 61.3% of his shots. Suppose you choose a random sample of 80 shots made by DeAndre during the 2013 season. Let X = the number of shots that scored points. Using the formulas, what is the mean?

49.04

The lifetime risk of developing pancreatic cancer is about one in 78 (1.28%). Let X = the number of people you ask before one says he or she has pancreatic cancer. The random variable X in this case includes only the number of trials that were failures and does not count the trial that was a success in finding a person who had the disease. X is a discrete random variable with a geometric distribution: X ~ G(178)or X ~ G(0.0128). What is the standard deviation of X?

77.62

The lifetime risk of developing pancreatic cancer is about one in 78 (1.28%). Let X = the number of people you ask before one says he or she has pancreatic cancer. The random variable X in this case includes only the number of trials that were failures and does not count the trial that was a success in finding a person who had the disease. X is a discrete random variable with a geometric distribution: X ~ G(178)or X ~ G(0.0128). What is the mean?

78.125

For the hypergeometric to work, the random variable must be _________ rather than continuous. One word answer

discrete

True or False: For the hypergeometric to work, the population must be divisible into two and only two independent subsets (aces and non-aces in our example). The random variable X = the number of items from the group of interest.

True

True or False: The Poisson distribution can be thought of as a clever way to convert a continuous random variable, usually time, into a discrete random variable by breaking up time into discrete independent intervals.

True

The Geometric Pdf tells us the probability that the first occurrence of success requires x number of ______ trials, each with success probability p.

independent

The switchboard in a Minneapolis law office gets an average of 5.5 incoming phone calls during the noon hour on Mondays. Experience shows that the existing staff can handle up to six calls in an hour. Let X = the number of calls received at noon. What is the probability that the office receives at most six calls at noon on Monday?

≈ 0.6860

The switchboard in a Minneapolis law office gets an average of 5.5 incoming phone calls during the noon hour on Mondays. Experience shows that the existing staff can handle up to six calls in an hour. Let X = the number of calls received at noon. What is the standard deviation of X?

≈ 2.3452

A nurse commented that when a patient the medical advice line claiming to have the flu, the chance that he or she has the flu (and not just a nasty cold) is only 4%. What is the standard deviation of the probability distribution function for a sample of 25 calls?

.980

Ellen has music practice three days a week. She practices for all of the three days 85% of the time, two days 8% of the time, one day 4% of the time, and no days 3% of the time. One week is selected at random. What values does X take on?

0,1,2,3

According to a recent Pew Research poll, 75% of millenials (people born between 1981 and 1995) have a profile on a social networking site. Let X = the number of millenials you ask until you find a person without a profile on a social networking site.What is the probability that you must ask 20 people to find one person without a social networking site?

0.0011

During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. DeAndre scored with 61.3% of his shots. Suppose you choose a random sample of 80 shots made by DeAndre during the 2013 season. Let X = the number of shots that scored points. What is the probability that DeAndre scored with 60 of these shots?

0.0036

The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 20-year period. Assume each year is independent. What is the probability that a person is audited more than twice.

0.0071

The switchboard in a Minneapolis law office gets an average of 5.5 incoming phone calls during the noon hour on Mondays. Experience shows that the existing staff can handle up to six calls in an hour. Let X = the number of calls received at noon. What is the probability that the office receives more than eight calls at noon?

0.1056

During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. DeAndre scored with 61.3% of his shots. Suppose you choose a random sample of 80 shots made by DeAndre during the 2013 season. Let X = the number of shots that scored points. What is the probability that DeAndre scored with more than 50 of these shots?

0.3718

The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 20-year period. Assume each year is independent. How many audits are expected in a 20-year period?

0.4

The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 20-year period. Assume each year is independent. What is the probability that a person is not audited at all?

0.6676

Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the time, two events 10% of the time, one event 5% of the time, and no events 5% of the time. Find the probability that Javier volunteers for at least one event each month. P(x > 0) = _______.

0.95

Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the time, two events 10% of the time, one event 5% of the time, and no events 5% of the time. Find the probability that Javier volunteers for at least one event each month. P(x > 0) = _______.

0.95

A nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only 4%. What is the probability that that 4 of the next 25 patients who call actually has the flu?

1.37%

In one of its Spring catalogs, L.L. Bean® advertised footwear on 29 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested in the number of pages that advertise footwear. Each page may be picked at most once. Calculate the standard deviation

1.5197

Which of the following does not have to be true in order for a Binomial Distribution to be applicable to a given problem?

Each trial is mutually exclusive

The literacy rate for a nation measures the proportion of people age 15 and over who can read and write. The literacy rate for women in The United Colonies of Independence is 12%. Let X = the number of women you ask until one says that she is literate. What is the probability that you must ask 10 women before one says she is literate?

P(x = 10) = 0.0380

The literacy rate for a nation measures the proportion of people age 15 and over who can read and write. The literacy rate for women in The United Colonies of Independence is 12%. Let X = the number of women you ask until one says that she is literate. What is the probability that you ask five women before one says she is literate?

P(x = 5) = .0720

In one of its spring catalogs, L.L. Bean advertised footwear on 29 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested in the number of pages that advertise footwear. Each page may be picked at most once. What is the Hypergeometric Distribution formula that tells us the probability that 4 pages out of the 20 surveyed advertise footwear?

P(x=4)=(29 combinatorial 4)(163 combinatorial 16) / (192 combinatorial 20)

A candy dish contains 30 jelly beans and 20 gumdrops. Ten candies are picked at random. What is the probability that 5 of the 10 are gumdrops? The two groups are jelly beans and gumdrops. Since the probability question asks for the probability of picking gumdrops, the group of interest (first group A in the formula) is gumdrops. The size of the group of interest (first group) is 30. The size of the second group is 20. The size of the sample is 10 (jelly beans or gumdrops). Let X = the number of gumdrops in the sample of 10. X takes on the values x = 0, 1, 2, ..., 10. What is the answer to the question "What is the probability of drawing 5 gumdrops in 10 picks from the dish?

P(x=5)=0.215

Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the time, two events 10% of the time, one event 5% of the time, and no events 5% of the time. What is the random variable X?

The number of events Javier volunteers for each month

The switchboard in a Minneapolis law office gets an average of 5.5 incoming phone calls during the noon hour on Mondays. Experience shows that the existing staff can handle up to six calls in an hour. Let X = the number of calls received at noon. Find the probability that the law office receives six calls at noon. What does this mean to the law office staff who get, on average, 5.5 incoming phone calls at noon?

There is a 15.7% probability that the law staff will receive more calls than they can handle.

In one of its spring catalogs, L.L. Bean advertised footwear on 29 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested in the number of page that advertise footwear. Each page may be picked at most once. In words, describe the random variable X

X = number of pages that advertise footwear

On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age. Assume the event occurs independently in any given day. What is the definition of the random variable X.

X = the number of U.S. teens who die from motor vehicle injuries per day

In one of its Spring catalogs, L.L. Bean® advertised footwear on 29 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested in the number of pages that advertise footwear. Each page may be picked at most once. In words, how could we define the random variable X.

X = the number of pages that advertise footwear

The literacy rate for a nation measures the proportion of people age 15 and over who can read and write. The literacy rate for women in The United Colonies of Independence is 12%. Let X = the number of women you ask until one says that she is literate. What is the probability distribution of X?

X ~ G(0.12)