Liberty University BUSI 230 review and exam 2 complete solutions answers and more!

Liberty University BUSI 230 review and exam 2 complete solutions answers and more!

For any distribution, what is the z-score corresponding to the mean?

What is the probability of randomly selecting a z-score less than z = −0.80 from a normal distribution?

Which of the following is not a continuous variable?

A normal distribution has a mean of μ = 80 with σ = 12. Find the following probabilities.

Any score with a value less than the population mean will have a negative z-score.

For a population with μ = 90 and σ = 25, find the z-score corresponding to each of the following X values.

If a binomial distribution has p = .30, then q = ____.

Consider the following two events for an individual.

A = owns a cell phone

B = owns a laptop computer

Translate each event into words.

(a) Ac

Answer

(b) A and B

Answer

(c) A or B

Answer

(d) A | B

Answer

(e) B | A

Does it pay to ask for a raise? A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one. According to the survey, of the women interviewed, 22% had asked for a raise, and of those women who had asked for a raise, 45% received the raise. If a woman is selected at random from the survey population of women, find the following probabilities. (Enter your answers to three decimal places.)

(a) P(woman asked for a raise)

Answer

(b) P(woman received raise, given she asked for one)

Answer

(c) P(woman asked for raise and received raise)

Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison ivy participated in the study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in the following table.

Let's use the following notation for the various events: W = washing oil off within 5 minutes, A = washing oil off after 5 minutes, N = no reaction, M = mild reaction, S = strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects. (Use 3 decimal places.)

(a) P(N)

P(M)

P(S)

(b) P(N | W)

 P(S | W)

(c) P(N | A)

 P(S | A)

(d) P(N and W)

 P(M and W)

(e) P(N or M).

Are the events N = no reaction and M = mild reaction mutually exclusive? Explain.

Answer

(f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain.

There is money to send two of seven city council members to a conference in Honolulu. All want to go, so they decide to choose the members to go to the conference by a random process. How many different combinations of two council members can be selected from the seven who want to go to the conference?

To open a combination lock, you turn the dial to the right and stop at a number; then you turn it to the left and stop at a second number. Finally, you turn the dial back to the right and stop at a third number. If you used the correct sequence of numbers, the lock opens. If the dial of the lock contains 7 numbers, 0 through 6, determine the number of different combinations possible for the lock. Note: The same number can be reused consecutively.

What are the requirements for a probability distribution

List the criteria for a binomial experiment. (Select all that apply.)

What does the random variable of a binomial experiment measure?

Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. Of special interest is the study of the number of moose killed by wolves. In the period from 1958 to 1974, there were 296 moose deaths identified as wolf kills. The age distribution of the kills is as follows.

(a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Use 3 decimal places.)

Calf (0.5 yr)

(1-5)

(6-10)

(11-15)

(16-20)

(b) Consider all ages in a class equal to the class midpoint. Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Use 2 decimal places.)

μ

σ

A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 17 randomly selected pens yields no more than two defective pens.

(a) Find the probability that this shipment is accepted if 10% of the total shipment is defective. (Use 3 decimal places.)

(b) Find the probability that this shipment is not accepted if 15% of the total shipment is defective. (Use 3 decimal places.)

According to Harper's Index, 55% of all federal inmates are serving time for drug dealing. A random sample of 20 federal inmates is selected.

(a) What is the probability that 10 or more are serving time for drug dealing? (Round your answer to three decimal places.)

(b) What is the probability that 5 or fewer are serving time for drug dealing? (Round your answer to three decimal places.)

(c) What is the expected number of inmates serving time for drug dealing? (Round your answer to one decimal place.)

Describe a normal probability distribution. (Select all that apply.)

According to the empirical rule, approximately what percentage of the area under a normal distribution lies within 1 standard deviation?

Within 2 standard deviations?

Answer

Within 3 standard deviations?

Given that x is a normal variable with mean μ = 45 and standard deviation σ = 6.6, find the following probabilities. (Round your answers to four decimal places.)

(a)  P(x ≤ 60)

(b)  P(x ≥ 50)

(c)  P(50 ≤ x ≤ 60)

Find z such that 23% of the area under the standard normal curve lies to the right of z. (Round your answer to two decimal places.)

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 9.9 minutes and a standard deviation of 2.9 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes

(b) longer than 5 minutes

(c) between 8 and 15 minutes

Many people consider their smart phone to be essential! Communication, news, Internet, entertainment, photos, and just keeping current are all conveniently possible with a smart phone. However, the battery better be charged or the phone is useless. Battery life of course depends on the frequency, duration, and type of use. One study involving heavy use of the phones showed the mean of the battery life to be 9.25 hours with a standard deviation of 3.5 hours. Then the battery needs to be recharged. Assume the battery life between charges is normally distributed.

(a) Find the probability that with heavy use, the battery life exceeds 10 hours. (Round your answer to four decimal places.)

(b) You are planning your recharging schedule so that the probability your phone will die is no more than 5%. After how many hours should you plan to recharge your phone? (Round your answer to the nearest tenth of an hour.)

The University of Montana ski team has ten entrants in a men's downhill ski event. The coach would like the first, second, and third places to go to the team members. In how many ways can the ten team entrants achieve first, second, and third places?

Are customers more loyal in the East or in the West? The following table is based on information from a recent study. The columns represent length of customer loyalty (in years) at a primary supermarket. The rows represent regions of the United States.

What is the probability that a customer chosen at random has the following characteristics? (Enter your answers as fractions.)

(a) has been loyal 10 to 14 years

Answer

(b) has been loyal 10 to 14 years, given that he or she is from the East

Answer

(c) has been loyal at least 10 years

Answer

(d) has been loyal at least 10 years, given that he or she is from the West

Answer

(e) is from the West, given that he or she has been loyal less than 1 year

Answer

(f) is from the South, given that he or she has been loyal less than 1 year

Answer

(g) has been loyal 1 or more years, given that he or she is from the East

Answer

(h) has been loyal 1 or more years, given that he or she is from the West

Answer

(i) Are the events from the East and loyal 15 or more years independent? Explain.

Sociologists say that 80% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that twelve married women are having coffee together one morning. Find the following probabilities. (Round your answers to three decimal places.)

(a) All of them dislike their mother-in-law.

(b) None of them dislike their mother-in-law.

Answer

(c) At least ten of them dislike their mother-in-law.

(d) No more than nine of them dislike their mother-in-law.

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 6.4 minutes and a standard deviation of 1.7 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

(a) the response time is between 3 and 8 minutes

(b) the response time is less than 3 minutes

Answer

(c) the response time is more than 8 minutes

A research team conducted a study showing that approximately 10% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 15 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.)

(a) at least one tie is too tight

(b) more than two ties are too tight

(c) no tie is too tight

(d) at least 13 ties are not too tight

At Litchfield College of Nursing, 87% of incoming freshmen nursing students are female and 13% are male. Recent records indicate that 60% of the entering female students will graduate with a BSN degree, while 90% of the male students will obtain a BSN degree. If an incoming freshman nursing student is selected at random, find the following probabilities. (Enter your answers to three decimal places.)

(a) P(student will graduate | student is female)

Answer

(b) P(student will graduate and student is female)

Answer

(c) P(student will graduate | student is male)

Answer

(d) P(student will graduate and student is male)

Answer

(e) P(student will graduate). Note that those who will graduate are either males who will graduate or females who will graduate.

Answer

(f) The events described the phrases "will graduate and is female" and "will graduate, given female" seem to be describing the same students. Why are the probabilities P(will graduate and is female) and P(will graduate | female) different?

A sales representative must visit seven cities. There are direct air connections between each of the cities. Use the multiplication rule of counting to determine the number of different choices the sales representative has for the order in which to visit the cities.

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 34 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 5 months, and the distribution of lifetimes is normal.

(a) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.)

(b) If Accrotime does not want to make refunds on more than 12% of the watches it makes, how long should the guarantee period be (to the nearest month)?

There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor; position 2 is the night nursing supervisor; and position 3 is the nursing coordinator position. There are 17 candidates qualified for all three of the positions. Determine the number of different ways the positions can be filled by these applicants.

Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.5 millimeters (mm) and a standard deviation of 0.9 mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.)

(a) the thickness is less than 3.0 mm

(b) the thickness is more than 7.0 mm

(c) the thickness is between 3.0 mm and 7.0 mm

When do creative people get their best ideas? USA Today did a survey of 966 inventors (who hold U.S. patents) and obtained the following information.

(a) Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a best idea during each time interval: from 6 A.M. to 12 noon, from 12 noon to 6 P.M., from 6 P.M. to 12 midnight, from 12 midnight to 6 A.M. (Enter your answers to 3 decimal places.)

(b) Do the probabilities add up to 1? Why should they?

What is the sample space in this problem?

During the Computer Daze special promotion, a customer purchasing a computer and printer is given a choice of seven free software packages. There are 10 different software packages from which to select. How many different groups of software packages can be selected?