BANA Exam II

The weight of an object is an example of

a continuous random variable

The number of customers that enter a store during one day is an example of

a discrete random variable

A normal distribution with a mean of 0 and a standard deviation of 1 is called

a standard normal distribution

A random variable that can assume only a finite number of values is referred to as a(n)

discrete random variable

The probability distribution that can be described by just one parameter is the​

exponential

To compute the probability that in a random sample of n elements, selected without replacement, we will obtain x successes, we would use the _____ probability distribution.

hypergeometric

The probability that a continuous random variable takes any specific value

is equal to zero

The key difference between the binomial and hypergeometric distribution is that, with the hypergeometric distribution, the

probability of success changes from trial to trial.

The probability distribution for the daily sales at Michael's Co. is given below. (In 1000s) 40 50 60 70 Probability 0.1 .04 .03 .23 The probability of having sales of at most $50,000 is

0.5

In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the

Poisson distribution

Two events with nonzero probabilities

cannot be both mutually exclusive and independent

A numerical description of the outcome of an experiment is called a

random variable

Emergency 911 calls to a small municipality in Idaho come in at the rate of one every four minutes. (a) What is the expected number of calls in one hour? (b) What is the probability of two calls in five minutes? (Round your answer to four decimal places.) (c) What is the probability of no calls in a five-minute period? (Round your answer to four decimal places.)

(A) 15 (b) 0.2238 (c) .2865

A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at the same frequency. (a) Develop a probability distribution for the duration of a service call. x 1 2 3 4 (c) Show that your probability distribution satisfies the conditions required for a discrete probability function. We have that f(x) ≥ 0 for x = 1, 2, 3, 4 and sigma f(x) = 1 so the probability distribution satisfies the required conditions for a valid discrete probability distribution. (d) What is the probability a service call will take three hours? (e) A service call has just come in, but the type of malfunction is unknown. It is 2:00 p.m. and service technicians usually get off at 5:00 p.m. What is the probability the service technician will have to work overtime to fix the machine today? .

(a) f(x) .25 .25 .25 .25 (d) .25 (e) .25

The following data were collected by counting the number of operating rooms in use at Tampa General Hospital over a 20-day period: On five of the days only one operating room was used, on eight of the days two were used, on four of the days three were used, and on three days all four of the hospital's operating rooms were used. (a) Use the relative frequency approach to construct an empirical discrete probability distribution for the number of operating rooms in use on any given day. X 1 2 3 4 (c)Show that your probability distribution satisfies the required conditions for a valid discrete probability distribution. We have that f(x) ≥ 0 for x = 1, 2, 3, 4 and sigma f(x) = 1 so the probability distribution satisfies the required conditions for a valid discrete probability distribution.

(a) f(x) .25 .4 .2 .15

Consider the experiment of tossing a coin twice. (Let H represent the head of the coin and T represent it's tail.) (a) List the experimental outcomes. (Select all that apply.) (b) Define a random variable that represents the number of heads occurring on the two tosses. The random variable x, where x = the number of heads that occur for two coin tosses , describes the scenario. (c) Show what value the random variable would assume for each of the experimental outcomes. (If an experimental outcome does not occur, enter NONE.) Outcome (H) (T) (H, H) (H, T) (T, H) (T, T) (d) Is this random variable discrete or continuous?

(a) (H, H)(H, T)(T, H)(T, T) (c) NONE NONE 2 1 1 0 (d) discrete

Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 10 passengers per minute. (Round your answers to six decimal places.) (a) Compute the probability of no arrivals in a one-minute period. (b) Compute the probability that three or fewer passengers arrive in a one-minute period. (c) Compute the probability of no arrivals in a 21-second period. (d) Compute the probability of at least one arrival in a 21-second period.

(a) .000045 (b) .010336 (c) .030197 (d) .969803

A center for medical services reported that there were 295,000 appeals for hospitalization and other services. For this group, 55% of first-round appeals were successful. Suppose 10 first-round appeals have just been received by a Medicare appeals office. (Round your answers to four decimal places.) (a) Compute the probability that none of the appeals will be successful. (b) Compute the probability that exactly one of the appeals will be successful. (c) What is the probability that at least two of the appeals will be successful? (d) What is the probability that more than half of the appeals will be successful?

(a) .0003 (b) .0042 (c) .9955 (d) .5044

A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. (Round your answers to four decimal places.) (a) Compute the probability that 2 or fewer will withdraw. (b) Compute the probability that exactly 4 will withdraw. (c) Compute the probability that more than 3 will withdraw. (d) Compute the expected number of withdrawals.

(a) .2061 (b) .2182 (c) .5886 (d) 4

Customer arrivals at a bank are random and independent; the probability of an arrival in any one-minute period is the same as the probability of an arrival in any other one-minute period. Answer the following questions, assuming a mean arrival rate of three customers per minute. (Round your answers to four decimal places.) (a) What is the probability of exactly three arrivals in a one-minute period? (b) What is the probability of at least three arrivals in a one-minute period?

(a) .2240 (b) .5768

The Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 21 restaurants located in a certain city, the average price of a dinner, including one drink and tip, was $48.60. You are leaving on a business trip to this city and will eat dinner at three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner. (Round your answers to four decimal places.) (a) What is the probability that none of the meals will exceed the cost covered by your company? (b) What is the probability that one of the meals will exceed the cost covered by your company? (c) What is the probability that two of the meals will exceed the cost covered by your company? (d) What is the probability that all three of the meals will exceed the cost covered by your company?

(a) .2737 (b) .4789 (c) .2211 (d) .0263

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces. (a) The process standard deviation is 0.1, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.9 or greater than 10.1 ounces will be classified as defects. (Round your answer to the nearest integer.) Calculate the probability of a defect. (Round your answer to four decimal places.) Calculate the expected number of defects for a 1,000-unit production run. (Round your answer to the nearest integer.) (b) Through process design improvements, the process standard deviation can be reduced to 0.05. Assume the process control remains the same, with weights less than 9.9 or greater than 10.1 ounces being classified as defects. Calculate the probability of a defect. (Round your answer to four decimal places.) Calculate the expected number of defects for a 1,000-unit production run. (Round your answer to the nearest integer.) (c) What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?

(a) .3173 and 317 (b) .0455 and 46 (c) Reducing the process standard deviation causes a substantial reduction in the number of defects

A consulting firm submitted a bid for a large research project. The firm's management initially felt they had a 50-50 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for 75% of the successful bids and 30% of the unsuccessful bids the agency requested additional information. (a) What is the prior probability of the bid being successful (that is, prior to the request for additional information)? (b) What is the conditional probability of a request for additional information given that the bid will ultimately be successful? (c) Compute the posterior probability that the bid will be successful given a request for additional information. (Round your answer to two decimal places.)

(a) .5 (b) .75 (c) .71

Suppose N = 10 and r = 3. Compute the hypergeometric probabilities for the following values of n and x. (Round your answers to four decimal places.) (a) n = 4, x = 1 (b) n = 2, x = 2 (c) n = 2, x = 0 (d) n = 4, x = 2 (e) n = 4, x = 4

(a) .5000 (b) .0667 (c) .4667 (d) .3000 (e) 0

A survey of magazine subscribers showed that 45.2% rented a car during the past 12 months for business reasons, 54% rented a car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for both business and personal reasons. (a) What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons? (b) What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons?

(a) .692 (b) .308

A deck of playing cards contains 52 cards, four of which are aces. (Round your answers to four decimal places.) (a) What is the probability that the deal of a five-card hand provides a pair of aces? (b) What is the probability that the deal of a five-card hand provides exactly one ace? (c) What is the probability that the deal of a five-card hand provides no aces? (d) What is the probability that the deal of a five-card hand provides at least one ace?

(a) 0.0399 (b) 0.2995 (c) 0.6588 (d) 0.3412

According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 emails per day.† Suppose for a particular office the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is three. (Round your answers to four decimal places.) (a) What is the probability of receiving no emails during an hour? (b) What is the probability of receiving at least three emails during an hour? (c) What is the expected number of emails received during 15 minutes? (d) What is the probability that no emails are received during 15 minutes?

(a) 0.0498 (b) 0.5768 (c) 0.75 (d) 0.4724

Phone calls arrive at the rate of 72 per hour at the reservation desk for Regional Airways. (Round your answers to four decimal places.) (a) Compute the probability of receiving three calls in a 5-minute interval of time. (b) Compute the probability of receiving exactly 10 calls in 15 minutes. (c) Suppose no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time? What is the probability that none will be waiting? (d) If no calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted by a call?

(a) 0.0892 (b) 0.0150 (c) 6 and .0025 (d) 0.0273

(a) A university knows from historical data that 25% of students in an introductory statistics class withdraw before completing the class. Assume that 16 students have registered for the course. What is the probability that exactly 2 will withdraw? (b) What is the probability that at least 3 but no more than 5 students will withdraw?

(a) 0.1336 (b) 0.6132

Blackjack, or twenty-one as it is frequently called, is a popular gambling game played in casinos. A player is dealt two cards. Face cards (jacks, queens, and kings) and tens have a point value of 10. Aces have a point value of 1 or 11. A 52-card deck contains 16 cards with a point value of 10 (jacks, queens, kings, and tens) and four aces. (Round your answers to four decimal places.) (a) What is the probability that both cards dealt are aces or 10-point cards? (b) What is the probability that both of the cards are aces? (c) What is the probability that both of the cards have a point value of 10? (d) A blackjack is a 10-point card and an ace for a value of 21. Use your answers to parts (a), (b), and (c) to determine the probability that a player is dealt blackjack. (Hint: Part (d) is not a hypergeometric problem. Develop your own logical relationship as to how the hypergeometric probabilities from parts (a), (b), and (c) can be combined to answer this question.)

(a) 0.1433 (b) 0.0045 (c) 0.0905 (d) 0.0483

You may need to use the appropriate appendix table to answer this question. The average return for large-cap domestic stock funds over three years was 14.4%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.4%. (a) What is the probability an individual large-cap domestic stock fund had a three-year return of at least 19%? (Round your answer to four decimal places.) (b) What is the probability an individual large-cap domestic stock fund had a three-year return of 10% or less? (Round your answer to four decimal places.) (c) How big does the return have to be to put a domestic stock fund in the top 15% for the three-year period? (Enter your answer as a percent and round your answer to two decimal places.)

(a) 0.1479 (b) 0.1587 (c) 18.96%

Intensive care units (ICUs) generally treat the sickest patients in a hospital. ICUs are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an ICU doctor or nurse. Therefore, it is important to use ICUs as efficiently as possible in a hospital. Suppose that a large-scale study of elderly ICU patients shows that the average length of stay in the ICU is 3.3 days. Assume that this length of stay in the ICU has an exponential distribution. (Round your answers to four decimal places.) (a) What is the probability that the length of stay in the ICU is one day or less? (b) What is the probability that the length of stay in the ICU is between two and three days? (c) What is the probability that the length of stay in the ICU is more than five days?

(a) 0.2614 (b) 0.1426 (c) 0.2198

A recent survey examined the use of social media platforms. Suppose the survey found that there is a 0.62 probability that a randomly selected person will use Facebook and a 0.27 probability that a randomly selected person will use LinkedIn. In addition, suppose there is a 0.24 probability that a randomly selected person will use both Facebook and LinkedIn. (a) What is the probability that a randomly selected person will use Facebook or LinkedIn? (b) What is the probability that a randomly selected person will not use either social media platform?

(a) 0.65 (b) 0.35

(a) What is the z-score for an upper-tail probability of 0.10? (b) What is the probability for the region −1.75 ≤ z ≤ 1.5?

(a) 1.282 (b) 0.893

PBS News Hour reported in 2014 that 39.4% of Americans between the ages of 25 and 64 have at least a two-year college degree.† Assume that 35 Americans between the ages of 25 and 64 are selected randomly. (a) What is the expected number of people with at least a two-year college-degree? (b) What are the variance and standard deviation for the number of people with at least a two-year college degree? (Round your answers to four decimal places.) variance 8.3567 standard deviation 2.8908

(a) 13.79

The following table provides a probability distribution for the random variable y. y f(y) 2 0.3 4 0.2 7 0.1 8 0.4 (a) Compute E(y). E(y) = b) Compute Var(y) and σ. (Round your answer for σ to two decimal places.) Var(y)= σ=

(a) 5.3 (b) Var(y)= 6.81 σ= 2.61

Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 152 probability. (a) List the sample points in the event an ace is selected. (b) List the sample points in the event a spade is selected. (c) List the sample points in the event a face card (jack, queen, or king) is selected. Find the probabilities associated with each of the events in parts (a), (b), and (c). (Enter your probabilities as fractions.) For (a):1/13 For (b):1/4 For (c):3/13

(a) S = {ace of clubs, ace of diamonds, ace of hearts, ace of spades} (b) S = {2 of spades, 3 of spades, ..., 10 of spades, jack of spades, queen of spades, king of spades, ace of spades} (c) S = {jack of clubs, jack of diamonds, jack of hearts, jack of spades, queen of clubs, queen of diamonds, queen of hearts, queen of spades, king of clubs, king of diamonds, king of hearts, king of spades}

Suppose that we have two events, A and B, with P(A) = 0.40, P(B) = 0.60, and P(A ∩ B) = 0.20. (a) Find P(A | B). (Round your answer to four decimal places.) P(A | B)= (b) Find P(B | A). P(B | A)= (c) Are A and B independent? Why or why not? A and B are not independent because P(A | B) ≠ P(A)

(a).3333 (b).5000

Consider a binomial experiment with two trials and p = 0.3. (b) Compute the probability of one success, f(1). f(1) = (c) Compute f(0). f(0) = (d) Compute f(2). f(2) = (e) Compute the probability of at least one success. (f) Compute the expected value, variance, and standard deviation. (Round your answer for the standard deviation to four decimal places.) expected value variance standard deviation

(b) .42 (c) .49 (d) .09 (e) .51 (f) ex. value: .6 variance: .42 std.: 0.6481

According to a 2018 survey by Bankrate.com, 20% of adults in the United States save nothing for retirement (CNBC website). Suppose that 15 adults in the United States are selected randomly. (a) Is the selection of the 15 adults a binomial experiment? Explain. The selection is a binomial experiment because the adults are selected randomly , p does not change from trial to trial, the trials are independent , and there are 2 outcomes possible. (b) What is the probability that all of the selected adults save nothing for retirement? (Round your answer to four decimal places.) (c) What is the probability that exactly nine of the selected adults save nothing for retirement? (Round your answer to four decimal places.) (d) What is the probability that at least one of the selected adults saves nothing for retirement? (Round your answer to four decimal places.)

(b) 0 (c) .0007 (d) .9648

The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. (b) What is the probability that the arrival time between vehicles is 12 seconds or less? (Round your answer to four decimal places.) (c) What is the probability that the arrival time between vehicles is 6 seconds or less? (Round your answer to four decimal places.) (d) What is the probability of 30 or more seconds between vehicle arrivals? (Round your answer to four decimal places.)

(b) 0.6321 (c) 0.3935 (d) 0.0821

Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle will require a nightly charge time of around 1 hour and 30 minutes (90 minutes) to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between 70 and 110 minutes. (a) Give a mathematical expression for the probability density function of battery recharging time for this scenario. f(x) = 1/40, 70 ≤ x ≤ 1100 0, elsewhere (b) What is the probability that the recharge time will be less than 101 minutes? (c) What is the probability that the recharge time required is at least 79 minutes? (Round your answer to four decimal places.) (d) What is the probability that the recharge time required is between 75 and 105 minutes?

(b) 0.775 (c) 0.775 (d) 0.75

General Hospital has noted that they admit an average of 8 patients per hour. Assuming a Poisson distribution, what is the probability that during the next two hours exactly 8 patients will be admitted? (Round your answer to three decimal places.)

.012

General Hospital has noted that they admit an average of 8 patients per hour. Assuming a Poisson distribution, what is the probability that during the next hour less then 3 patients will be admitted? (Round your answer to three decimal places.)

.014

The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. What is the probability that a randomly selected tire will have a life of of less than 30,000 miles?Round your answer to three decimal places.

.023

The weight of football players for a team is normally distributed with a mean of 275 pounds and a standard deviation of 50 pounds.The probability of a player weighing more than 350 pounds is(Use Excel and round your answer to three decimal places.)

.067

An insurance company has determined that on average they receive nine claims per week at their Cincinnati office. Assume that the claims distribution can be described by a Poisson distribution. What is the probability that they will receive nine claims in a week? (Round your answer to three decimal places.)

.132

Suppose you first randomly sample one card from a deck of 52. Then, without putting the card back in the deck you sample a second and then (again without replacing cards) a third. Given this sampling procedure, what is the probability that at least one ace will be in the three sampled cards? Four of the 52 cards in the deck are aces. Round your answer to three decimal places.

.217

The student body of a large university consists of 60% female students. A random sample of 8 students is selected.What is the probability that among the students in the sample exactly four are female? Use an Excel function and round your answer to three decimal places.

.232

The student body of a large university consists of 60% female students. A random sample of 8 students is selected.What is the probability that among the students in the sample at most four are female? Use an Excel function and round your answer to three decimal places.

.406

A new automated production process averages 2.5 breakdowns per day. Because of the cost associated with a breakdown, management is concerned about the possibility of having three or more breakdowns during a day. Assume that breakdowns occur randomly, that the probability of a breakdown is the same for any two time intervals of equal length, and that breakdowns in one period are independent of breakdowns in other periods. What is the probability of having three or more breakdowns during a day? (Round your answer to four decimal places.)

.4562

The ages of students at a university are normally distributed with a mean of 21. What proportion of the student body is at least 21 years old?Round your answer to two decimal places.

.5

The assembly time for a product is uniformly distributed between 6 to 10 minutes.The probability of assembling the product between 7 to 9 minutes is(Round your answer to two decimal places.)

.5

The student body of a large university consists of 60% female students. A random sample of 8 students is selected.What is the probability that among the students in the sample more than four are female? Use an Excel function and round your answer to three decimal places

.594

The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. What proportion of the tires will have a life of 34,000 to 46,000 miles?Round your answer to three decimal places.

.77

Forty percent of the students who enroll in a statistics course go to the statistics laboratory on a regular basis. Past data indicates that 65% of those students who use the lab on a regular basis make a grade of A in the course. On the other hand, only 10% of students who do not go to the lab on a regular basis make a grade of A. If a particular student made an A, determine the probability that she or he used the lab on a regular basis. Enter your answer rounded to four decimal places. Use a tree diagram to answer this question.

.8125

The student body of a large university consists of 60% female students. A random sample of 8 students is selected.What is the probability that among the students in the sample at least four are female? Use an Excel function and round your answer to three decimal places.

.826

The life expectancy of computer terminals is normally distributed with a mean of 4 years and a standard deviation of 1 year. What is the probability that a terminal will last 5 years or less? Use Excel and round your answer to three decimals.

.841

The weight of football players for a team is normally distributed with a mean of 275 pounds and a standard deviation of 50 pounds.The probability of a player weighing between 200 and 350 pounds is(Round your answer to three decimal places.)

.866

The assembly time for a product is uniformly distributed between 6 to 10 minutes.The probability of assembling the product in less than 6 minutes is(Round your answer to one decimal place.)

0

If A and B are mutually exclusive events with P(A) = 0.295, P(B) = 0.32, then P(A | B) =

0.0000

Cars arrive at a car wash randomly and independently; the probability of an arrival is the same for any two time intervals of equal length. The mean arrival rate is 15 cars per hour. What is the probability that 20 or more cars will arrive during any given hour of operation? (Round your answer to six decimal places.)

0.1248

The time required to load a truck is exponentially distributed with a mean of 15 minutes. What is the probability that a truck will be loaded in 10 to 20 minutes? Enter your answer as a decimal not as a percent and round your answer to 3 decimal places.

0.25

The time required to load a truck is exponentially distributed with a mean of 15 minutes. What is the probability that a truck will be loaded in 20 minutes or more? Enter your answer as a decimal not as a percent and round your answer to 3 decimal places.

0.264

The time required to load a truck is exponentially distributed with a mean of 15 minutes. What is the probability that a truck will be loaded in 10 minutes or less? Enter your answer as a decimal not as a percent and round your answer to 3 decimal places.

0.487

The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number of Goals 0 1 2 3 4 Probability 0.05 0.15 0.35 0.30 0.15 What is the probability that in a given game the Lions will score less than 3 goals?

0.55

If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A union B) =

0.68

A class of 50 consists of 60% business students. A random sample of 8 students is selected.What is the probability that among the students in the sample at most four are non-business students? Use an Excel function and round your answer to three decimal places.

0.847

The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number of Goals 0 1 2 3 4 Probability 0.05 0.15 0.35 0.30 0.15 What is the probability that in a given game the Lions will score at least 1 goal?

0.95

(b) What is the z-value for a one-tail (upper) probability of 5%?

1.65

How many permutations of three items can be selected from a group of six?

120

An experiment has three steps with five outcomes possible for the first step, four outcomes possible for the second step, and seven outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?

140

The weight of football players is normally distributed with a mean of 275 pounds and a standard deviation of 50 pounds. What is the minimum weight of the middle 95% of the players?Round your answer to one decimal place.

177

Random variable x has the probability function f(x) = X/6, for x = 1, 2 or 3 The expected value of x is

2.333

The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number of Goals 0 1 2 3 4 Probability 0.05 0.15 0.35 0.30 0.15 The expected number of goals per game is

2.35

How many ways can three items be selected from a group of six items?

20

Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. How many different random samples of four accounts are possible?

230300

The student body of a large university consists of 60% female students. A random sample of 8 students is selected.What is the expected number of females selected? Round your answer to one decimal place.

4.8

"DRUGS R US" is a large manufacturer of various kinds of liquid vitamins. The quality control department has noted that the bottles of vitamins marked 6 ounces vary in content with a mean of 6 ounces and a standard deviation of 0.3 ounces. Assume the contents of the bottles are normally distributed. Ninety-five percent of the bottles will contain at least how many ounces? Round your answer to 2 decimal places.

5.51

In a binomial experiment consisting of five trials, the number of different values that x (the number of successes) can assume is​

6

"DRUGS R US" is a large manufacturer of various kinds of liquid vitamins. The quality control department has noted that the bottles of vitamins marked 6 ounces vary in content with a mean of 6 ounces and a standard deviation of 0.3 ounces. Assume the contents of the bottles are normally distributed. Ninety-five percent of the bottles will contain less than how many ounces? Round your answer to 2 decimal places.

6.49

The assembly time for a product is uniformly distributed between 6 to 10 minutes.The expected assembly time (in minutes) is(Round your answer to one decimal place.)

8

A professor at a local community college noted that the grades of his students were normally distributed with a mean of 74 and a standard deviation of 10. The professor has informed us that 6.3 percent of his students received A's while only 2.5 percent of his students failed the course and received F's. What is the minimum score needed to earn an A? Enter your answer rounded to one decimal place.

89.3

What probability range is associated with z = ±1.96?

95%

Use the letters A, B, C, D, E, and F to identify the items, and list each of the different combinations of three items. (Enter your answers as a comma-separated list. Enter three unspaced capital letters for each combination.)

ABC,\ ABD,\ ABE,\ ABF,\ ACD,\ ACE,\ ACF,\ ADE,\ ADF,\ AEF,\ BCD,\ BCE,\ BCF,\ BDE,\ BDF,\ BEF,\ CDE,\ CDF,\ CEF,\ DEF

Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F. (Enter your answers as a comma-separated list. Enter three unspaced capital letters for each permutation.)

BDF,\ BFD,\ DBF,\ DFB,\ FBD,\ FDB

A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? We would assign a probability of .2 to the design 1 outcome, .2 to design 2, .2 to design 3, .2 to design 4, and .2 to design 5. In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Design # of times preferred 1 5 2 15 3 30 4 40 5 10 Do the data confirm the belief that one design is just as likely to be selected as another? Explain.

No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely.

The company identified in Chapter 5, Statistics in Practice is

Not a company but precinct polling locations

The company identified in Chapter 6, Statistics in Practice is

Proctor & Gamble

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a

continuous random variable

A measure of the average value of a random variable is called a(n

expected value

The Statistics in Practice example in Chapter 5 focuses on

polling booths or machines

The function that defines the probability distribution of a continuous random variable is a

probability density function

Chapter 5 focuses on

probability distributions

Chapter 6 focuses on

probability distributions

The Statistics in Practice example in Chapter 6 identifies an application concerned with

raw material prices

An experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 10 times, E2 occurred 11 times, and E3 occurred 29 times. Assign probabilities to the outcomes. P(E1)=.2 P(E2)=.22 P(E3)=.58 What method did you use?

relative frequency method

Bayes' theorem is used to compute

the posterior probabilities

If two events are independent, then

the product of their probabilities gives their intersection

Larger values of the standard deviation result in a normal curve that is

wider and flatter