Survey of Data Analytics - Chapter 5 Quiz

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: Number Sold. 0. 1. 2 Frequency. 10. 10. 25 What is the expected number of cars sold by the salesperson during a week? a. 0.8 b. 1.5 c. 1 d. 0

A

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: Number Sold. 0. 1. 2 Frequency. 10. 10. 25 What is the standard deviation of the number of cars sold by the salesperson during a week? a. 0.75 b. 0.80 c. 1 d. 0.56

A

The number of homes sold by a realtor during a month has the following probability distribution: Number Sold. 0. 1. 2 Probability. 0.20 0.30. 0.50 What is the standard deviation of the number of homes sold by the realtor during a month? a. 0.78 b. 0.61 c. 1.47 d. 1.30

A

Cars arrive randomly at a tollbooth at a rate of 20 cars per 15 minutes during rush hour. What is the probability that exactly five cars will arrive over a five-minute interval during rush hour? a. 0.1395 b. 0.1517 c. 0.6017 d. 0.2268

A For a Poisson random variable X, the probability of x successes over a given interval of time or space is calculated asP(X=x)=(e^−μμ^x)/x!; μ− the mean number of successes; e ≈ 2.718. The Excel's function POISSON.DIST can be used. The Excel function used is =POISSON.DIST(5,20/3,FALSE) = 0.1395.

A consumer who is risk averse is best characterized as __________. a. a consumer who demands a positive expected gain as compensation for taking risk b. a consumer who is indifferent to risk c. a consumer who completely ignores risk and makes his or her decisions based solely on expected values d. a consumer who may accept a risky prospect even if the expected gain is negative

A In general, consumers are risk averse and expect a reward for taking risk. A risk-averse consumer demands a positive expected gain as compensation for taking risk.

Consider the following probability distribution. xi 0. 1. 2. 3 P(X = xi) 0.4. 0.3. 0.1. 0.2 The expected value is _____. a. 1.1 b. 0.7 c. 1.7 d. 0.1

A The expected value of X is calculated as E(X) = μ = ∑xi P(X = xi). E(X) = 0 × 0.4 + 1 × 0.3 + 2 × 0.1 + 3 × 0.2 = 1.1

Consider the following cumulative distribution function for the discrete random variable X. x 1. 2. 3. 4 P(X ≤ x). 0.30. 0.44. 0.72. 1.00 What is the probability that X equals 2? a. 0.14 b. 0.44 c. 0.56 d. 0.30

A The probability distribution of a discrete random variable is a list of the values with the associated probabilities.The cumulative distribution function of X is defined as P(X ≤ x). The cumulative probability representation is convenient when we are interested in finding the probability over a range of values rather than a specific value.P(X = 2) = P(X ≤ 2) − P(X ≤ 1) = 0.44 − 0.30 = 0.14

According to geologists, the San Francisco Bay Area experiences ten earthquakes with a magnitude of 5.8 or greater every 100 years. What is the standard deviation of the number of earthquakes with a magnitude of 5.8 or greater striking the San Francisco Bay Area in the next 40 years? a. 4.000 b. 2.000 c. 4.236 d. 10.000

A The standard deviation of a Poisson random variable is computed as SD(X)=σ=√μ. 10 earthquakes/100 years relates to 4 earthquakes/40 years. σ = √4 = 2.000.

According to geologists, the San Francisco Bay Area experiences ten earthquakes with a magnitude of 6.3 or greater every 100 years. What is the standard deviation of the number of earthquakes with a magnitude of 6.3 or greater striking the San Francisco Bay Area in the next 40 years? a. 4.000 b. 10.000 c. 4.236. d. 2.000

A The standard deviation of a Poisson random variable is computed as SD(X)=σ=√μ. 10 earthquakes/100 years relates to 4 earthquakes/40 years. σ = √4 = 2.000.

According to the Department of Transportation, 26% of domestic flights were delayed in the last year at JFK airport. Three flights are randomly selected at JFK. What is the probability that all three flights are delayed? a. 0.0356 b. 0.0176 c. 0.0370 d. 0.0384

B For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated asP(X=x)=(n/x)p^xq^(n−x)=n!/x!(n−x)!=p^xq^(n−x). Calculate P(X = 3). The Excel's function BINOM.DIST can be used.The Excel function used is =BINOM.DIST(3,3,0.26,FALSE) = 0.0176.

On a particular production line, the likelihood that a light bulb is defective is 13%. Five light bulbs are randomly selected. What is the probability that at most 3 of the light bulbs will be defective? a. 0.0102 b. 0.9987 c. 0.0112. d. 0.9882

B For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated asP(X=x)=(n/x)p^xq^(n−x)=n!/x!(n−x)!=p^xq^(n−x). Calculate P(X = 3). The Excel's function BINOM.DIST can be used.The Excel function used is =BINOM.DIST(3,5,0.13,TRUE) = .0.9987

Consider the following probability distribution. xi 0. 1 2. 3 P(X = xi). 0.3 0.1. 0.4. 0.2 The expected value is _____. a. 2.1 b 1.5 c. 0.5 d. 1.1

B The expected value of X is calculated as E(X) = μ = ∑xi P(X = xi). E(X) = 0 × 0.3 + 1 × 0.1 + 2 × 0.4 + 3 × 0.2 = 1.5

An analyst believes that a stock's return depends on the state of the economy, for which she has estimated the following probabilities: State of the Economy Probability. Return Good 0.60. 15% Normal 0.30. 10% Poor 0.10 -2% According to the analyst's estimates, the expected return of the stock is ____. a. 15.0% b. 11.8% c. 7.8% d. 11.4%

B The expected value of X is calculated as E(X) = μ = ∑xi P(X = xi). E(X) = 15 × 0.60 + 10 × 0.30 + (−2) × 0.10 = 11.8

The number of homes sold by a realtor during a month has the following probability distribution: Number Sold. 0 1 2 Probability. 0.40 0.10. 0.50 What is the standard deviation of the number of homes sold by the realtor during a month? a. 1.10 b 0.94 c. 0.89 d. 1.63

B The standard deviation of the discrete random variable X is calculated as SD(X)=σ=√(σ^2). The variance of the discrete random variable X is calculated as Var(X) = σ^2 = ∑(xi − μ)^2 P(X = xi). E(X) = 0 × 0.40 + 1 × 0.10 + 2 × 0.50 = 1.10. Var(X) = (0 − 1.10)^2 × 0.40 + (1 − 1.10)^2 × 0.10 + (2 − 1.10)^2 × 0.50 = 0.89 SD(X)=√0.89 = 0.943

Cars arrive randomly at a tollbooth at a rate of 45 cars per 20 minutes during rush hour. What is the probability that exactly five cars will arrive over a five-minute interval during rush hour? a. 0.4817 b. 0.1068 c. 0.0195 d. 0.0317

C For a Poisson random variable X, the probability of x successes over a given interval of time or space is calculated asP(X=x)=(e^−μμ^x)/x!; μ− the mean number of successes; e = 2.25. The Excel's function POISSON.DIST can be used. The Excel function used is =POISSON.DIST(5,11.25,FALSE) = 0.0195.

On a particular production line, the likelihood that a light bulb is defective is 11%. Five light bulbs are randomly selected. What is the probability that at most 2 of the light bulbs will be defective? a. 0.0003 b. 0.0013 c. 0.9888 d. 0.9783

C For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated asP(X=x)=(n/x)p^xq^(n−x)=n!/x!(n−x)!=p^xq^(n−x). Calculate P(X = 3). The Excel's function BINOM.DIST can be used.The Excel function used is =BINOM.DIST(2,5,0.11,TRUE) = 0.0176.

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? a. 0.45 b. 0.75 c. 0.25 d. 0.35

C The probability distribution of a discrete random variable is a list of the values with the associated probabilities.The cumulative distribution function of X is defined as P(X ≤ x). The cumulative probability representation is convenient when we are interested in finding the probability over a range of values rather than a specific value.P(X ≤ 3) = 1 −P(X ≤ 3) = 1 − 0.75 = 0.25

According to the Department of Transportation, 30% of domestic flights were delayed in the last year at JFK airport. Three flights are randomly selected at JFK. What is the probability that all three flights are delayed? a. 0.0450 b. 0.0464 c. 0.0478 d. 0.0270

D For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated asP(X=x)=(n/x)p^xq^(n−x)=n!/x!(n−x)!=p^xq^(n−x). Calculate P(X = 3). The Excel's function BINOM.DIST can be used.The Excel function used is =BINOM.DIST(3,3,0.30,FALSE) = 0.0270.