Liberty University BUSI 230 week 4 exercises 5.1-6.3 complete solutions answers and more!

Liberty University BUSI 230 week 4 exercises 5.1-6.3 complete solutions answers and more!

Question 1

Which of the following are continuous variables, and which are discrete?

(a) number of traffic fatalities per year in the state of Florida

Answer

(b) distance a golf ball travels after being hit with a driver

Answer

(c) time required to drive from home to college on any given day

Answer

(d) number of ships in Pearl Harbor on any given day

Answer

(e) your weight before breakfast each morning

Answer

Question 2

Consider each distribution. Determine if it is a valid probability distribution or not, and explain your answer.

x

P(x)

x

P(x)

Question 3

Consider each distribution. Determine if it is a valid probability distribution or not, and explain your answer.

x

P(x)

Compute the expected value of the distribution.

Answer

Compute the standard deviation of the distribution. (Round your answer to four decimal places.)

Question 4

A particular lake is known to be one of the best places to catch a certain type of fish. In this table, x = number of fish caught in a 6-hour period. The percentage data are the percentages of fishermen who caught x fish in a 6-hour period while fishing from shore.

x

%

(a) Convert the percentages to probabilities and make a histogram of the probability distribution.

(b) Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6-hour period. (Round your answer to two decimal places.)

Answer

(c) Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period. (Round your answer to two decimal places.)

Answer

(d) Compute μ, the expected value of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Round your answer to two decimal places.)

Answer

(e) Compute σ, the standard deviation of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Round your answer to three decimal places.)

Answer

Question 5

What does the random variable for a binomial experiment of n trials measure?

Question 6

For a binomial experiment, how many outcomes are possible for each trial? What are the possible outcomes?

Question 7

Consider a binomial experiment with n = 7 trials where the probability of success on a single trial is p = 0.40. (Round your answers to three decimal places.)

(a) Find P(r = 0).

(b) Find P(r ≥ 1) by using the complement rule.

Question 8

Richard has just been given a 8-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all eight questions, find the indicated probabilities. (Round your answers to three decimal places.)

(a) What is the probability that he will answer all questions correctly?

Answer

(b) What is the probability that he will answer all questions incorrectly?

Answer

(c) What is the probability that he will answer at least one of the questions correctly? Compute this probability two ways. First, use the rule for mutually exclusive events and the probabilities shown in the binomial probability distribution table.

Answer

Then use the fact that P(r ≥ 1) = 1 − P(r = 0).

Answer

Compare the two results. Should they be equal? Are they equal? If not, how do you account for the difference?

Answer

(d) What is the probability that Richard will answer at least half the questions correctly?

Question 9

The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 20% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of six adult friends, what is the probability of the following? (Round your answers to three decimal places.)

(a) no one has done a one-time fling

Answer

(b) at least one person has done a one-time fling

Answer

(c) no more than two people have done a one-time fling

Question 10

Trevor is interested in purchasing the local hardware/sporting goods store in the small town of Dove Creek, Montana. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 55% of the business days it is open. Estimate the probability that the store will gross over $850 for the following. (Round your answers to three decimal places.)

(a) at least 3 out of 5 business days

(b) at least 6 out of 10 business days

(c) fewer than 5 out of 10 business days

(d) fewer than 6 out of the next 20 business days

If the outcome described in part (d) actually occurred, might it shake your confidence in the statement p = 0.55? Might it make you suspect that p is less than 0.55? Explain.

(e) more than 17 out of the next 20 business days

If the outcome described in part (e) actually occurred, might you suspect that p is greater than 0.55? Explain.

Question 11

Are your finances, buying habits, medical records, and phone calls really private? A real concern for many adults is that computers and the Internet are reducing privacy. A survey conducted by Peter D. Hart Research Associates for the Shell Poll was reported in USA Today. According to the survey, 39% of adults are concerned that employers are monitoring phone calls. Use the binomial distribution formula to calculate the probability of the following.

(a) Out of six adults, none is concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

(b) Out of six adults, all are concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

(c) Out of six adults, exactly four are concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

Question 12

What does the expected value of a binomial distribution with n trials tell you?

Question 13

Consider a binomial distribution of 200 trials with expected value 80 and standard deviation of about 6.9. Use the criterion that it is unusual to have data values more than 2.5 standard deviations above the mean or 2.5 standard deviations below the mean to answer the following questions.

1 standard deviation

2 standard deviations

Any number that is more than 13.8 away from the mean of 80 would be unusual.

Expected would be in the range

Unusual would be a score

(a) Would it be unusual to have more than 120 successes out of 200 trials? Explain.

Answer

(b) Would it be unusual to have fewer than 40 successes out of 200 trials? Explain.

Answer

(c) Would it be unusual to have from 70 to 90 successes out of 200 trials? Explain.

Question 14

Let r be a binomial random variable representing the number of successes out of n trials.

(a) Explain why the sample space for r consists of the set {0, 1, 2, ..., n} and why the sum of the probabilities of all the entries in the entire sample space must be 1.

Answer

(b) Explain why P(r ≥ 1) = 1 − P(0).

Answer

(c) Explain why P(r ≥ 2) = 1 − P(0) − P(1).

Answer

(d) Explain why P(r ≥ m) = 1 − P(0) − P(1) − ... − P(m − 1) for 1 ≤ m ≤ n.

Question 15

Look at the two normal curves in the figures below.

Which has the larger standard deviation?

Answer

What is the mean of the curve in Figure (a)?

Answer

What is the mean of the curve in Figure (b)?

Question 16

Sketch a normal curve with the following parameters.

(a) mean of 15 and standard deviation of 2

(b) mean of 15 and standard deviation of 3

(c) mean of 12 and standard deviation of 2

(d) mean of 12 and standard deviation of 3

(e) Consider two normal curves. If the first one has a larger mean than the second one, must it have a larger standard deviation as well? Explain your answer.

Question 17

(a) What percentage of the area under the normal curve lies to the left of μ?

Answer

(b) What percentage of the area under the normal curve lies between μ − σ and μ + σ?

Answer

(c) What percentage of the area under the normal curve lies between μ − 3σ and μ + 3σ?

Question 18

What percentage of the area under the normal curve lies as given below?

(a) to the right of μ

Answer

(b) between μ – 2σ and μ + 2σ

Answer

(c) to the right of μ + 3σ (Use 2 decimal places.)

Question 19

Assuming that the heights of college women are normally distributed with mean 67 inches and standard deviation 2.8 inches, answer the following questions. (Hint: Use the figure below with mean μ and standard deviation σ.)

(a) What percentage of women are taller than 67 inches?

Answer

(b) What percentage of women are shorter than 67 inches?

Answer

(c) What percentage of women are between 64.2 inches and 69.8 inches?

Answer

(d) What percentage of women are between 61.4 and 72.6 inches?

Question 20

The incubation time for a breed of chicks is normally distributed with a mean of 25 days and standard deviation of approximately 2 days. Look at the figure below and answer the following questions. If 1000 eggs are being incubated, how many chicks do we expect will hatch in the following time periods? (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.)

(a) in 21 to 29 days

Answer

(b) in 23 to 27 days

Answer

(c) in 25 days or fewer

Answer

(d) in 19 to 31 days

Question 21

A normal distribution has μ = 32 and σ = 5.

(a) Find the z score corresponding to x = 27.

(b) Find the z score corresponding to x = 43.

(c) Find the raw score corresponding to z = −2.

(d) Find the raw score corresponding to z = 1.7.

Question 22

Raul received a score of 71 on a history test for which the class mean was 70 with a standard deviation of 9. He received a score of 76 on a biology test for which the class mean was 70 with standard deviation 4. On which test did he do better relative to the rest of the class?

Question 23

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

Shade the corresponding area under the standard normal curve.

Question 24

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

Shade the corresponding area under the standard normal curve.

Question 25

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

Shade the corresponding area under the standard normal curve.

Question 26

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

Shade the corresponding area under the standard normal curve.

Question 27

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(−2.10 ≤ z ≤ −0.40) =

Shade the corresponding area under the standard normal curve.

Question 28

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

Question 29

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

Question 30

Find z such that 3.4% of the standard normal curve lies to the right of z. (Round your answer to two decimal places.)

Sketch the area described.

Question 31

Find z such that 6% of the standard normal curve lies to the left of z. (Round your answer to three decimal places.)

Sketch the area described.

Question 32

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 82 and standard deviation σ = 24. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)

(a) x is more than 60

(b) x is less than 110

(c) x is between 60 and 110

(d) x is greater than 125 (borderline diabetes starts at 125)

Question 33

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean μ = 42 and standard deviation σ = 14. Find the following probabilities. (Round your answers to four decimal places.)

(a) x is less than 60

(b) x is greater than 16

(c) x is between 16 and 60

(d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)

Question 34

Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 46.2 months and a standard deviation of 7.9 months.

(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.)

(b) If Quick Start does not want to make refunds for more than 7% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?