Stat 210 Test 2

According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. What is the standard deviation of the number of earthquakes with a magnitude of 6.5 or greater strike the San Fransisco Bay Area in the next 40 years? A. 1.414 B. 2.000 C. 2.236 D. 5.000

A

Which if the following can be represented by a continuous random variable? A. The average temperature in Tampa, Florida, during the month of July B. The number of typos found selected page of this test bank. C. The number of students who will get financial assistance in a group of 50 randomly selected students D. The number of customers who visit a department store between 10AM and 11AM on Mondays.

A

Which of the following can be represented by a continuous random variable? A. The time of a flight between Chicago and NY B. The number of defective light bulbs in a sample of five. C. The number of arrivals to a drive-through bank window in a four-hour period D. The score of a randomly selected student on a five-question multiple-choice quiz

A

Which of the following can be represented by a discrete random variable? A. The number of obtained spots when rolling a six-sided die B. The height of college students C. The average outside temperature taken every day for two weeks. D. The finishing time of participants in a cross country meet

A

Let P(A n B)= 0.3, and P(A n B^c)= 0.15 and P(A^c n B)= 0.35 Compute P(A^c n B^c) A. 0.2 B. 0.5 C. 0.65 D. 0.70

A P(A)= P(A n B) + P(A n B^c) = P(A|B)P(B) + P(A|B^c)P(B^c)

Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. What is the probability that both fund A and B will rise in price? A. 0.24 B. 0.40 C. 0.76 D. 1.00

A P(B|A)= P(A n B) / P(A)

According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. What is the probability that one or more earthquakes with a magnitude of 6.5 or greater strike the San Fransisco Bay Area in the next 40 years? A. 0.0488 B. 0.1353 C. 0.4878 D. 0.9512

A POISSON.DIST

On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. What is the probability that two light bulbs will be defective? A. 0.0105 B. 0.0746 C. 0.3151 D. 0.5987

B

Suppose that 60% of the students do homework regularly. It is also known that 80% of the students who had been doing homework regularly, end up doing well in the course. Only 20% of students who had not been doing homework regularly end up doing well in the course. Given that a student did well in the course, what is the probability that the student had been doing homework regularly? A. 0.286 B. 0.857 C. 0.143 D. 0.429

B

An urn contains 12 balls, five of which are red. The selection of a red ball is desired and is therefore considered to be a success. If a person draws three balls from the urn, what is the probability of the two successes? A. 0.1591 B. 0.3182 C. 0.6810 D. 0.8409

B HYPGEOM.DIST

Peter applied to an accounting firm and a consulting firm. He knows that 30% of similarly qualified applicants receive job offers from the accounting firm while only 20% of similarly qualified applicants receive job offers from the consulting firm. Assume that receiving an offer from one firm is independent of receiving an offer from the other. What is the probability that both firms offer Peter a job? A. 0.05 B. 0.06 C. 0.44 D. 0.50

B Joint probability for two independent events is the product of the individual probabilities.

Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. What is the probability that at least one of the funds will rise in price? A. 0.24 B. 0.36 C. 0.60 D. 0.76

B P(A U B)= P(A) + P(B) - P(A n B)

How many ways can a committee of four students be selected from a 15-member club? A. 15!/44! B. 15! / (11! * 4!) C. 15 * 14 * 13 D. B and C

B. nCx= n! / (n-x)!x!

A sample space contains _____. A. outcomes of the relevant events B. several outcomes of an experiment C. all possible outcomes of an experiment D. one of several outcomes of an experiment

C

If A and B are independent events, which of the following is correct? A. P(A U B)= 0 B. P(A n B)= 0 C. P(A|B)= P(A) D. P(A U B)= P(A) + P(B)

C

On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. What are the mean and variance of the number of defective light bulbs? A. 0.475 and 0.475 B. 0.475 and 0.6892 C. 0.50 and 0.475 D. 0.50 and 0.6892

C

Thirty percent of the CFA candidates have a degree in economics. A random sample of three CFA candidates is selected. What is the probability that at least one of them has a degree in economics? A. 0.300 B. 0.343 C. 0.657 D. 0.900

C

We can think of the expected value of a random variable X as A. the long-run average of the random variable values generated over 100 independent repetitions B. the long-run average of the random variable values generated over 1,000 independent repetitions C. the long-run average of the random variable values generated over infinitely many independent repetitions D. the long-run average of the random variable values generated over a finite number of independent repetitions

C

What is probability? A. Any value between 0 and 1 is always treated as a probability of an event B. A numerical value assigned to an event that measures the number of its occurrences. C. A value between 0 and 1 assigned to an event that measures the likelihood of its occurrence. D. A value between 0 and 1 assigned to an event that measures the unlikelihood of its occurrence

C

When some objects are randomly selected, which of the following is true? A. The order in which objects are selected matters in combinations B. The order in which objects are selected does not matter in permutations C. The order in which objects are selected does not matter in combinations D. The order in which objects are selected matters in both permutations and combinations

C

Which of the following can be represented by a discrete random variable? A. The circumference of a randomly generated circle B. The time of a flight between Chicago and NY C. The number of defective lightbulbs in a sample of five D. The average distance achieved in a series of long jumps

C

Which of the following is true about the hypergeometric distribution? A. The trials are independent and the probability of success may change from trial to trial B. The trials are independent and the probability of success does not change from trial to trial C. The trials are not independent and the probability of success may change from trial to trial D. The trials are not independent and the probability of success does not change from trial to trial

C

Which of the following represents a subjective probability? A. The probability of rolling a 2 on a single die is one in six. B. Based on a conducted experiment, the probability of tossing a head on an unfair coin is 0.6 C. A skier believes she has a 10% chance of winning a gold medal D. Based on past observation, a manager believes there is a three-in-five chance of retaining an employee for at least a year

C

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that at least one in a random sample of four calculators is defective? A. 0.0010 B. 0.2916 C. 0.3439 D. 0.6561

C BINOM.DIST

Thirty percent of the CFA candidates have a degree in economics. A random sample of three CFA candidates is selected. What is the probability that none of them have a degree in economics? A. 0.027 B. 0.300 C. 0.343 D. 0.900

C BINOM.DIST

The likelihood of Company A's stock price rising is 20% and the likelihood of Company B's stock price rising is 30%. Assume that the returns of Company A and Company B stock are independent of each other. The probability that the stock price of at least one of the companies will rise is _____. A. 6% B. 10% C. 44% D. 50%

C P(A U B)= P(A) + P(B) - P (A n B)

Let P(A)= 0.4, P(B|A)= 0.5, and P(B|A^c)= 0.25 Compute P(A|B) A. 0.20 B. 0.35 C. 0.57 D. 0.80

C P(B|A)= P(A n B) / P(A n B) + P(A n B^c)

According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. What is the probability that more than 2 earthquakes with a magnitude of 6.5 or greater strike the San Fransisco Bay Area in the next 40 years? A. 0.1353 B. 0.2706 C. 0.3233 D. 0.8754

C POISSON.DIST

According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. What is the probability that no earthquakes with a magnitude of 6.5 or greater strike the San Fransisco Bay Area in the next 40 years? A. 0.0067 B. 0.0337 C. 0.1353 D. 0.2707

C POISSON.DIST

How many project teams composed of five students can be created out of a class of 10 students? A. 10 B. 50 C. 252 D. 30,240

C nCx= n! / (n-x)!x!

Let P(A)= 0.6, P(B)= 0.5, and P((A U B)^c)= 0.1 Calculate P(A|B). A. 0.20 B. 0.33 C. 0.40 D. Not enough info to calculate

C complement rule: P(A)= 1 - P(A^c) addition rule: P(A U B)= P(A) + P(B) - P(A n B)

Let P(A)= 0.3 and P(B)= 0.4 Suppose A and B are independent. What is the value of P(B|A)? A. 0.12 B. 0.3 C. 0.4 D. 0.7

C Independent: P(B|A)= P(B)

On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. What is the probability that two light bulbs will be defective? A. 0.0105 B. 0.0746 C. 0.3151 D. 0.5987

D

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that none in a random sample of four calculators is defective? A. 0.0010 B. 0.2916 C. 0.3439 D. 0.6561

D BINOM.DIST

Romi, a production manager, is trying to improve the efficiency of his assembly line. He knows that the machine is set up correctly only 70% of the time. He also knows that if the machine is set up correctly, its will produce good parts 95% of the time, but if set up incorrectly it will produce good parts only 40% of the time. Romi starts the machine and produces one part before he begins the production run. He finds the first part to be good. What is the revised probability that the machine was set up correctly? A. 12% B. 33.5% C. 66.5% D. 84.7%

D Bayes's theorem: P(B|A)= P(A|B)P(B) / P(A|B)P(B) + P(A|B^c)P(B^c)

An urn contains 12 balls, five of which are red. The selection of a red ball is desired and is therefore considered to be a success. If three balls are selected, what is the expected value of the distribution of the number of selected red balls? A. 0.4167 B. 0.8333 C. 0.5833 D. 1.2500

D HYPGEOM.DIST

Let A and B be two independent events with P(A)= 0.40 and P(B)= 0.20. Which of the following is correct? A. P(B|A)= 0.40 B. P(A|B)= 0.80 C. P(A n B)= 0 D. P(A U B)= 0.52

D P(A U B)= P(A) + P(B) - P(A n B)

Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. What is the probability that neither fund will rise in price? A. 0.24 B. 0.36 C. 0.40 D. 0.64

D P(A U B)= P(A) + P(B) - P(A n B) P(A)= 1 - P(A^c)

Let P(A n B)= 0.3 and P(A n B^c)= 0.15 Compute P(B|A) A. 0.33 B. 0.45 C. 0.5 D. 0.67

D P(A)= P(A n B) + P(A n B^c) = P(A|B)P(B) + P(A|B^c)P(B^c)

Let P(A)= 0.4, P(B|A)= 0.5 and P(B|A^c)= 0.25 Compute P(B) A. 0.125 B. 0.15 C. 0.20 D. 0.35

D P(A)= P(A n B) + P(A n B^c)P(A|B)P(B) + P(A|B^c)P(B^c)

How many ways can a potential four-letter word, whether or not it has a meaning, be created out of 10 available different letters? A. 4 * 3 * 2 * 1 B. 10 * 9 * 8 * 7 / (4 * 3 * 2) C. 10 * 9 * 8 * 7 * 6 * 5 / (4 * 3 * 2) D. 10 * 9 * 8 * 7

D nPx= n! / (n-x)!

0!=0 T or F

F

A probability distribution of a continuous random variable X gives the probability that X takes on a particular value x, P(X=x). T or F.

F

Combinations are used when the order in which different objects are arranged matters. T or F

F

A Poisson random variable counts the number of successes (occurrences of a certain event) over a given interval of time or space. T or F

T

Given two random variables X and Y, the expected value of their sum, E(X + Y), is equal to the sum of their individual expected values, E(X) and E(Y). T or F

T

Permutations are used when the order in which different objects are arranged matters. T or F

T

Testing whether the computer is infected or not would be best described using binomial probability distribution. T or F

T

The risk of the portfolio depends not only on the individual risks of the assets but also on the _____ between the asset returns.

covariance

A(n) _____ probability is calculated as the relative frequency with which an event occurs.

empirical

The hypergeometric probability distribution is appropriate in applications where we cannot assume the trials are _____.

independent