Practice Problems---BU255 Midterm 2023Fall 2023-10-24--- Solution

 What is the variance of the sample below? Firm No. of Partners Deloitte & Touche 2,618 6,853,924 1,290,874.7 7 Ernst & Young 2,118 4,485,924 404,708.07 PricewaterhouseCoopers 2,027 4,108,729 297,206.73 KPMG 1,535 2,356,225 2,826.70 Grant Thornton 312 97,344 1,368,510.0 0 BDO Seidman 281 78,961 1,442,000.6 1 Summations 8,891 17,981,10 7 4,806,126.8 8 Firm No. of Partners Deloitte & Touche 2,618 6,853,924 1,290,874.7 7 Ernst & Young 2,118 4,485,924 404,708.07 PricewaterhouseCoopers 2,027 4,108,729 297,206.73 KPMG 1,535 2,356,225 2,826.70 Grant Thornton 312 97,344 1,368,510.0 0 BDO Seidman 281 78,961 1,442,000.6 1 Summations 8,891 17,981,10 7 4,806,126.8 8 a. 1,481.83 b. 961,225.38 c. 980.42 d. 17,981.107

 One of the integers from 1 to 10 is selected at random. If A is the event that we select an even number and B is the event that we select a number greater than 6. What is the probability of A or B? a) 2/10 b) 7/10 c) 4/10 d) 5/10

 A survey found that 43% of Canadians expect to save more money next year than they did last year. 45% plan to reduce debt next year. Of those who expect to save money, 81% plan to reduce debt next year. A Canadian is selected at random. What is the probability that this person neither expects to save more money nor plans to reduce debt? a) 0.3483 b) 0.537 c) 0.5755 d) 0.4683

n = 20 Probability x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.122 0.012 0.001 0.000 0.000 0.000 0.000 0.000 0.000 1 0.270 0.058 0.007 0.000 0.000 0.000 0.000 0.000 0.000 2 0.285 0.137 0.028 0.003 0.000 0.000 0.000 0.000 0.000 3 0.190 0.205 0.072 0.012 0.001 0.000 0.000 0.000 0.000 4 0.090 0.218 0.130 0.035 0.005 0.000 0.000 0.000 0.000 5 0.032 0.175 0.179 0.075 0.015 0.001 0.000 0.000 0.000 6 0.009 0.109 0.192 0.124 0.037 0.005 0.000 0.000 0.000 7 0.002 0.055 0.164 0.166 0.074 0.015 0.001 0.000 0.000 8 0.000 0.022 0.114 0.180 0.120 0.035 0.004 0.000 0.000 9 0.000 0.007 0.065 0.160 0.160 0.071 0.012 0.000 0.000 10 0.000 0.002 0.031 0.117 0.176 0.117 0.031 0.002 0.000 11 0.000 0.000 0.012 0.071 0.160 0.160 0.065 0.007 0.000 12 0.000 0.000 0.004 0.035 0.120 0.180 0.114 0.022 0.000 13 0.000 0.000 0.001 0.015 0.074 0.166 0.164 0.055 0.002 14 0.000 0.000 0.000 0.005 0.037 0.124 0.192 0.109 0.009 15 0.000 0.000 0.000 0.001 0.015 0.075 0.179 0.175 0.032 16 0.000 0.000 0.000 0.000 0.005 0.035 0.130 0.218 0.090 17 0.000 0.000 0.000 0.000 0.001 0.012 0.072 0.205 0.190 18 0.000 0.000 0.000 0.000 0.000 0.003 0.028 0.137 0.285 19 0.000 0.000 0.000 0.000 0.000 0.000 0.007 0.058 0.270 20 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.012 0.122

 A real estate office sells 1.6 houses on an average weekday and sales of houses on weekdays are Poisson distributed. What is the probability of selling 10 or more houses in a day? a) 0.0002 b) 0.2019 c) 0.0000 d) 0.9998

 If 10% of a population of parts is defective, what is the probability of randomly selecting 80 parts and finding that 12 or more parts are defective? a) 0.5681 b) 0.4319 c) 0.9319 d) 0.0681

 Suppose a course’s final exam marks from the last year follow a normal distribution. The mean and standard deviation are 70 and 5, respectively. Approximately 16.0% of all course marks will be higher than which value? a) 65 b) 75 c) 80 d) 85

 The sample space S consists of whole numbers starting at 1 and strictly less than 15. Let event A = the even numbers and event B = the numbers strictly greater than 13. What is P(A and B’)? a) 0.0 b) 1/14 c) 6/14 d) 8/14

 The sample space S consists of whole numbers starting at 1 and strictly less than 15. Let event A = the even numbers and event B = the numbers strictly greater than 13. What is P(B |A)? a) 0.0 b) 1/14 c) 1/7 d) 8/14

 Let event G = taking a math class. Let event H = taking a science class. Suppose P(G) = 0.6, P(H) = 0.5 , and P(G ∩ H) = 0.3. Which of the following statements is true? a) G and H are independent b) G and H are dependent c) G and H are mutually exclusive d) G and H are collectively exhaustive

In a basketball arena, • 70% of the fans are rooting for the home team. • 25% of the fans are wearing blue. • 21% of the fans are wearing blue and are rooting for the away team. • Of the fans rooting for the away team, 70% are wearing blue. Let A be the event that a fan is rooting for the away team. Let B be the event that a fan is wearing blue. What is P(A’ and B)? a) 0.04 b) 0.09 c) 0.66 d) 0.70

A drug test proposed by a company tests positive 99% of the time on drug consumers, and it tests negative 95% of the time on non- consumers. Let’s say the drug is consumed by 1% of the general population. If a random person tests negative for the drug, what is the probability that (s)he is a drug consumer? a) 0.0000 b) 0.0001 c) 0.9405 d) 0.9406

Studies show that about one woman in seven (approximately 14.3%) will develop breast cancer in her lifetime. Suppose that of those women who develop breast cancer, a test is negative 2% of the time. Also suppose that in the general population of women, the test for breast cancer is negative about 85% of the time. Suppose one woman is selected at random out of the population. What is the probability that her test result is positive? a) 0.0000 b) 0.1400 c) 0.1500 d) 0.8500

During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. Suppose DeAndre scored with 60% of his shots. Suppose you choose a random sample of 20 shots made by DeAndre during the 2013 season. Let X = the number of shots that scored points. What is the standard deviation of X? a) 0.6 b) 2.2 c) 4.8 d) 20

n = 20 Probability x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.122 0.012 0.001 0.000 0.000 0.000 0.000 0.000 0.000 1 0.270 0.058 0.007 0.000 0.000 0.000 0.000 0.000 0.000 2 0.285 0.137 0.028 0.003 0.000 0.000 0.000 0.000 0.000 3 0.190 0.205 0.072 0.012 0.001 0.000 0.000 0.000 0.000 4 0.090 0.218 0.130 0.035 0.005 0.000 0.000 0.000 0.000 5 0.032 0.175 0.179 0.075 0.015 0.001 0.000 0.000 0.000 6 0.009 0.109 0.192 0.124 0.037 0.005 0.000 0.000 0.000 7 0.002 0.055 0.164 0.166 0.074 0.015 0.001 0.000 0.000 8 0.000 0.022 0.114 0.180 0.120 0.035 0.004 0.000 0.000 9 0.000 0.007 0.065 0.160 0.160 0.071 0.012 0.000 0.000 10 0.000 0.002 0.031 0.117 0.176 0.117 0.031 0.002 0.000 11 0.000 0.000 0.012 0.071 0.160 0.160 0.065 0.007 0.000 12 0.000 0.000 0.004 0.035 0.120 0.180 0.114 0.022 0.000 13 0.000 0.000 0.001 0.015 0.074 0.166 0.164 0.055 0.002 14 0.000 0.000 0.000 0.005 0.037 0.124 0.192 0.109 0.009 15 0.000 0.000 0.000 0.001 0.015 0.075 0.179 0.175 0.032 16 0.000 0.000 0.000 0.000 0.005 0.035 0.130 0.218 0.090 17 0.000 0.000 0.000 0.000 0.001 0.012 0.072 0.205 0.190 18 0.000 0.000 0.000 0.000 0.000 0.003 0.028 0.137 0.285 19 0.000 0.000 0.000 0.000 0.000 0.000 0.007 0.058 0.270 20 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.012 0.122

During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. Suppose DeAndre scored with 60% of his shots. Suppose you choose a random sample of 20 shots made by DeAndre during the 2013 season. Let X = the number of shots that scored points. What is probability that DeAndre made less than 12 shots? a) 0.10 b) 0.20 c) 0.40 d) 0.50

During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. Suppose DeAndre scored with 60% of his shots. Suppose you choose a random sample of 20 shots made by DeAndre during the 2013 season. Let X = the number of shots that scored points. What is probability that DeAndre made between 5 and 15 shots (inclusive)? a) 0.12 b) 0.22 c) 0.95 d) 0.99

A bank expects to receive 10 bad checks per day, on average. What is the probability of the bank getting exactly 10 bad checks on any given day? Assuming that the number of bad checks received per day follows a Poisson distribution. a) 0.125 b) 0.165 c) 0.465 d) None of the above.

The maternity ward at Dr. Jose Fabella Memorial Hospital in Manila in the Philippines is one of the busiest in the world with an average of 60 births per day (24 hours). What is the probability that the number of births in a random hour is more than two? a) 0.336 b) 0.456 c) 0.544 d) 0.666

The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 15 minutes. What is the probability that a person waits between 10 and 20 minutes? a) 0.00 b) 0.33 c) 0.67 d) 1.00

Let X = amount of time (in minutes) a postal clerk spends with a customer. The time is known from historical data to follow the Exponential distribution with an average amount of time equal to four minutes. What is probability that P(3.90 < X < 4.10)? a) 0.00 b) 0.02 c) 0.06 d) 0.10

On average, a pair of running shoes can last 18 months if used every day. The length of time running shoes last is exponentially distributed. What is the probability that a pair of running shoes last more than 15 months? a) 0.13 b) 0.23 c) 0.43 d) 0.50

The final exam scores in a statistics class were normally distributed with a mean of 63 and a standard deviation of 5. What is the probability that a randomly selected student scored between 64 and 70 on the exam? a) 0.92 b) 0.58 c) 0.34 d) 1.00

A personal computer is used for office work at home, research, communication, personal finances, education, entertainment, social networking, and a myriad of other things. Suppose that the average number of hours a household personal computer is used for entertainment is two hours per day. Assume the times for entertainment are normally distributed and the standard deviation for the times is half an hour. What is the probability a household personal computer is used for entertainment more than 2.2 hours per day? a) 0.34 b) 0.66 c) 0.31 d) 1.00

A personal computer is used for office work at home, research, communication, personal finances, education, entertainment, social networking, and a myriad of other things. Suppose that the average number of hours a household personal computer is used for entertainment is two hours per day. Assume the times for entertainment are normally distributed and the standard deviation for the times is half an hour. What is the probability a household personal computer is used for entertainment more than 5.2 hours per day? a) 0.34 b) 0.66 c) 0.31 d) 0.00

Statistics Canada reports that per capita solid waste generation in Canada amounted to 2.7 kg per day. Suppose the daily amount of waste generated per person is normally distributed with a mean of 2.7 kg and a standard deviation of 0.5 kg. Of the daily amounts of waste generated per person, 60% would be more than what amount? a) 2.70 b) 2.83 c) 2.57 d) None of the above.

Suppose that the mean expenditure per customer at a grocery store is $90.00, with a standard deviation of $9.00. If a random sample of 40 customers is taken, what is the probability that the sample average expenditure per customer for this sample will less than $88.00? a) 0.08 b) 0.38 c) 0.88 d) 0.92

Suppose that the mean expenditure per customer at a grocery store is $90.00, with a standard deviation of $9.00. If a random sample of 40 customers is taken, 90% of the time this sample mean expenditure will be lower than which amount? a) 90.0 b) 9.0 c) 91.8 d) 88.2

If 10% of a population of products is defective, what is the probability of randomly selecting 100 products and finding that between 10 and 12 (inclusive) products are defective? a) 0.12 b) 0.88 c) 0.75 d) 0.25

Candidate Liu believes se will receive 58% of the total votes cast in her riding. However, in an attempt to validate this figure, her pollster contacts a random sample of 600 registered voters in the riding. The poll results show that 330 of the voters say they are committed to voting for her. If she actually has 58% of the total vote, what is the probability of getting a sample proportion this small or smaller? a) 0.58 b) 0.42 c) 0.07 d) 0.93

Which of the following is an example of a continuous distribution? a) Volume of water in a water bottle b) Number of people who prefer diet coke over regular coke c) Number of people who voted for a given candidate for mayor d) Number of people entering a store in a given hour.

During a recent winter, the temperature stayed below zero for ten days (ranging from -22 to -3). The standard deviation of the temperatures over the ten-day period a) Is negative because all the temperatures are negative b) Can be either positive or negative c) Cannot be computed since all numbers are negative d) Must be greater than zero

If 80% of people in a class play soccer, 50% play basketball and 40% play both soccer and basketball: a) Someone playing soccer increases the chance of playing basketball. b) Someone playing soccer does not affect the chance of playing basketball. c) Someone playing soccer decreases the chance of playing basketball. d) We need more information to infer any of the above.

A list of the top 10 highest paid athletes is an example of what kind of data? a) Nominal b) Ordinal c) Interval d) Ratio