BANA 1 - Exam2

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.)

0.132

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?

0.023

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

0.067

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

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.)

0.140

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

0.594

A new automated production process averages 3.5 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.)

0.6792

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

0.68

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.

0.77

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

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

expected value

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 company identified in Chapter 5, Statistics in Practice is

not a company but precinct polling locations

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

probability of success changes from trial to trial.

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

wider and flatter

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

0.50

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

0.0000

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

0

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.

0.232

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.)

0.25

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.

0.406

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.

0.50

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.

0.8125

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.

0.826

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.

0.841

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 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

0.866

What is the probability for the region −1.75 ≤ z ≤ 1.5?

0.893

What is the z-score for an upper-tail probability of 0.10?

1.282

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?

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 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 place

6.49

The assembly time for a product is uniformly distributed between 6 to 10 minutes.The expected assembly time (in minutes) is

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

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 seven. (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 expected number of emails received during 15 minutes?

A. 0.0009 B. 0.9704 C. 1.75 D. 0.0175

A center for medical services reported that there were 295,000 appeals for hospitalization and other services. For this group, 45% 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. 0.0025 B. 0.0207 C. 0.9767 D. 0.2250

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

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? C2. 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 C2. 0.0183 D. 0.1209

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. A. 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

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. 0.2240 B. 0.5768

.The Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 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. 0.2637 B. 0.4945 C. 0.2198 D. 0.0220

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 17%? (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 10% for the three-year period? (Enter your answer as a percent and round your answer to two decimal places.)

A. 0.2773 B. ???? C. 20.03

A university found that 10% 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. 0.6769 B. 0.0898 C. 0.133 D. 2

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 45 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.)

A. 17.73 B. Variance: 10.7444 Standard deviation: 3.2779

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

The company identified in Chapter 6, Statistics in Practice is

Proctor & Gamble

Two events with nonzero probabilities

cannot be both mutually exclusive and independent

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 numerical description of the outcome of an experiment is called a

random variable

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

raw material prices

Bayes' theorem is used to compute

the posterior probabilities

If two events are independent, then

the product of their probabilities gives their intersection.