Busi. Statistics Exam 2

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?

.06 P(Accounting∩Consulting) = 0.30 × 0.20 = 0.06

Consider the following cumulative distribution function for the discrete random variable X. x. 1. 2. 3. 4. P(X ≤ x). 0.03 0.44 0.72 1.00 What is the probability that X equals 2?

.14 P(X = 2) = P(X ≤ 2) − P(X ≤ 1) = 0.44 − 0.30 = 0.14

Consider the following cumulative distribution function for the discrete random variable X. x 1. 2. 3. 4. 5. P(X ≤ x)0.10. 0.35. 0.75. 0.85 1.00 What is the probability that X is greater than 3?

.25 P(X ≤ 3) = 1 −P(X ≤ 3) = 1 − 0.75 = 0.25

Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced The probability that a respondent read a book in the last month and is at least 30 years old is the closest to _______.

.33 P(Yes∩30+)=65/200=0.33

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

.4

The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. What is the probability that a randomly selected customer prefers vanilla?

.40 P(Vanilla)=20+40/150=0.40

The probability that a normal random variable is less than its mean is ______.

.5

Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced. The probability that a respondent is at least 30 years old is the closest to ______.

.50 P(30+)=100/200=0.50

What is the standard deviation of the number of homes sold by the realtor during a month?

.75 E(X) = 0 × 0.20 + 1 × 0.40 + 2 × 0.40 = 1.2 Var(X) = (0 − 1.2)2 × 0.20 + (1 − 1.2)2 × 0.40 + (2 − 1.2)2 × 0.40 = 0.56 SD(X)=√0.56=0.75

What is the standard deviation of the number of cars sold by the salesperson during a week?

.75 E(X) = 0 × 10/25 + 1 × 10/25 + 2 × 5/25 = 0.80Var(X) = (0 − 0.80)2 × 10/25 + (1 − 0.80)2 × 10/25 + (2 − 0.80)2 × 5/25 = 0.56 SD(X)=sq root 0.56=0.75

For a particular clothing store, a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. Suppose six customers are randomly selected and are mailed $10-off coupons. What is the expected number of coupons that will be redeemed?

.96 E(X) = μ = np. μ = 6 × 0.16 = 0.96

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take exactly 3.7 hours to construct a soapbox derby car.

0.0000

The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35, and those 35 years of age or older. Find the probability that an individual prefers biking given that he or she is 35 years old or older.

0.1698 P(Biking∣∣35 years or older)=27/159=0.1698

Alex is in a hurry to get to work and is rushing to catch the bus. She knows that the bus arrives every six minutes during rush hour, but does not know the exact times the bus is due. She realizes that from the time she arrives at the stop, the amount of time that she will have to wait follows a uniform distribution with a lower bound of 0 minutes and an upper bound of six minutes. What is the probability that she will have to wait less than two minutes?

0.3333

The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Find the probability that an individual prefers running.

0.3915 P(Running)=202/516=0.3915

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 bulbs?

0.50 and 0.475 the Excel function used is μ = 10 × 0.05 = 0.50; σ2 = 10 × 0.05 × 0.95 = 0.475

What are the two key properties of a discrete probability distribution?

0≤P (X = x) ≤1 and ∑P (X = xi ) = 1

What is the expected number of homes sold by the realtor during a month?

1.2 E(X) = 0 × 0.20 + 1 × 0.40 + 2 × 0.40 = 1.2

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 striking the San Francisco Bay Area in the next 40 years?

1.414 SD(X)=σ=√U SD(X)=σ=μ. 5 earthquakes/100 years relates to 2 earthquakes/40 yearsσ = 2‾√2 = 1.414

According to a Department of Labor report, the city of Detroit had a 20% unemployment rate in May. Eight working-age residents were chosen at random. What was the expected number of unemployed residents, when eight working-age residents were randomly selected?

1.6 E(X) = μ = np. The Excel function used is μ = 8 × 0.20 = 1.6

The expected value is _____.

1.90 E(X) = 0 × 0.10 + 1 × 0.20 + 2 × 0.40 + 3 × 0.30 = 1.9

The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is ______.

1/(b − a) between a and b, and zero otherwise

How many parameters are needed to fully describe any normal distribution?

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 expected value of the number of earthquakes with a magnitude of 6.5 or greater striking the San Francisco Bay Area in the next 40 years?

2.00 E(X) = µ. So, 5 earthquakes/100 years relates to 2 earthquakes/40 years. E(X) = 2

A daily mail is delivered to your house between 1:00 p.m. and 5:00 p.m. Assume delivery times follow the continuous uniform distribution. Determine the percentage of mail deliveries that are made after 4:00 p.m.

25%

According to a study by the Centers for Disease Control and Prevention, about 33% of U.S. births are Caesarean deliveries. Suppose seven expectant mothers are randomly selected. The expected number of mothers who will not have a Caesarean delivery is ______.

4.69 E(X) = μ = np. μ = 7 × (1 − 0.33) = 4.69

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 ______.

44% P(A∪B) = 0.20 + 0.30 − 0.20 × 0.30 = 0.44.

5! is equal to _______.

5 × 4 × 3 × 2 × 1

Sarah's portfolio has an expected annual return at 8%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has an approximate ______.

50% chance that the actual return will be greater than 8%

For any normally distributed random variable with mean μand standard deviation σ, the percent of the observations that fall between [μ − 2σ, μ + 2σ] is the closest to ______.

95%

You work in marketing for a company that produces work boots. Quality control has sent you a memo detailing the length of time before the boots wear out under heavy use. They find that the boots wear out in an average of 208 days, but the exact amount of time varies, following a normal distribution with a standard deviation of 14 days. For an upcoming ad campaign, you need to know the percent of the pairs that last longer than six months—that is, 180 days. Use the empirical rule to approximate this percent.

97.5%

How would you characterize a consumer who is risk loving?

A consumer who may accept a risky prospect even if the expected gain is negative.

Which of the following is correct?

A continuous random variable has a probability density function, and a discrete random variable has a probability mass function.

Which of the following represents a subjective probability?

A skier believes she has a 10% chance of winning a gold medal.

What is probability?

A value between 0 and 1 assigned to an event that measures the likelihood of its occurrence.

What is a simple event?

An event that contains only one outcome of a sample space

Which of the following statements is the most accurate about a binomial random variable?

It counts the number of successes in a given number of trials.

Which of the following statements is the most accurate about a Poisson random variable?

It counts the number of successes in a specified time or space interval.

Which of the following sets of outcomes described below in I and II represent mutually exclusive events? "Your final course grade is an A"; "Your final course grade is a B." "Your final course grade is an A"; "Your final course grade is a Pass."

Only I represents mutually exclusive events.

If A and B are independent events, which of the following is correct?

P(A|B)=P(A)

Let A and B be two independent events with P(A) = 0.40 and P(B) = 0.20. Which of the following is correct?

P(A∪B)=0.52 P(A∪B) = 0.40 + 0.20 − 0.40 × 0.20 = 0.52

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X < 20) related to P(X < 16)?

P(X < 20) is greater than P(X < 16).

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X > 16) related to P(X < 16)?

P(X > 16) is greater than P(X < 16)

The cumulative distribution function F(x) of a continuous random variable X with the probability density function f(x) is which of the following?

The area under f over all values that are x or less.

Which of the following does not represent a continuous random variable?

The number of customer arrivals to a bank between 10 am and 11 am.

Which of the following is best described as a Poisson variable?

The number of positive reviews in a week.

When some objects are randomly selected, which of the following is true?

The order in which objects are selected does not matter in combinations.

Which of the following is FALSE about a continuous random variable?

The probability that its value is within a specific interval is equal to one.

Which of the following is an example of a uniformly distributed random variable?

The scheduled arrival time of a cable technician.

What does it mean when we say that the tails of the normal curve are asymptotic to the x axis?

The tails get closer and closer to the x axis but never touch it.

Let X be normally distributed with mean μ and standard deviation σ > 0. Which of the following is false about the zvalue corresponding to a given x value?

The z value corresponding to a given value of xassumes any value between 0 and 1.

A consumer who is risk neutral is best characterized as ______________________________________________________.

a consumer who completely ignores risk and makes his or her decisions based solely on expected values

A consumer who is risk averse is best characterized as __________.

a consumer who demands a positive expected gain as compensation for taking risk

Mutually exclusive events _____________.

do not share common outcomes

A sample space contains _________________.

all possible outcomes of an experiment.

A probability based on logical analysis rather than on observation or personal judgment is best referred to as a(n) _______________.

classical probability

Which of the following is not a characteristic of a probability density function f(x)?

f(x) is symmetric around the mean.

A continuous random variable has the uniform distribution on the interval [a, b] if its probability density function f(x) ______.

is constant for all x between a and b, and 0 otherwise

We can think of the expected value of a random variable X as ________.

the long-run average of the random variable values generated over infinitely many independent repetitions

Events are collectively exhaustive if _____________.

they contain all outcomes of an experiment