Unit 2 Test STA 2023 McGraw Hill
0! = 0.
False By definition 0!=1
The starting salary of an administrative assistant is normally distributed with a mean of $50,000 and a standard deviation of $2,500. We know that the probability of a randomly selected administrative assistant making a salary between μ - x and μ + x is 0.7416. Find the salary range referred to in this statement.
$47,175 to $52,825
The odds for encountering rain on a 500-mile car trip are three to one. What is the probability of rain on this trip?
0.75
How many ways can a potential four-letter word, whether or not it has a meaning, be created out of 10 available different letters?
10 * 9 * 8 * 7
For an experiment in which a single die is rolled, the sample space is __________.
{2, 1, 3, 6, 5, 4}.
Forty-four percent of consumers with credit cards carry balances from month to month. Four consumers with credit cards are randomly selected. What is the probability that all consumers carry a credit card balance?
0.0375
Forty-four percent of consumers with credit cards carry balances from month to month. Four consumers with credit cards are randomly selected. What is the probability that all consumers carry a credit card balance?
0.0375 For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated as 2formula16.mml Calculate P(X = 4). The Excel's function BINOM.DIST can be used.
The odds for encountering rain on a 500-mile car trip are three to one. What is the probability of rain on this trip?
0.75 Given odds for event A occurring of "a to b," the probability of A is a/a+b
How many ways can a committee of four students be selected from a 15-member club?
15!/(11! ×4!) nCx: combination formula n=15 x=4
A small company that manufactures juggling equipment makes seven different types of clubs. The company wants to start an ad campaign that emphasizes the myriad combinations the avid juggler can create with the company's clubs. If a juggler wishes to juggle four clubs, each of a different type, how many different combinations of the company's clubs can he or she make?
35 The number of combinations is computed as formula161.mml
The total probability rule is useful only when the unconditional probability is expressed in terms of probabilities conditional on two mutually exclusive and exhaustive events.
False The total probability rule expresses the unconditional probability of an event, in terms of probabilities conditional on various exclusive and exhaustive events.
The total probability rule is defined as P(A) = P(A formula10.mml B) P(Aformula10.mmlformula11.mml)
False The total probability rule is defined as P(A) = P(A1formula8.mmlB) + P(A1formula8.mmlformula9.mml).
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.
For the sample space S = {apple pie, cherry pie, peach pie, pumpkin pie}, what is the complement of A = {pumpkin pie, cherry pie}?
The complement of event A, Ac, is the event consisting of all outcomes in the sample space S that are not in A. {apple pie, peach pie}
Which of the following is true about the hypergeometric distribution?
The trials are not independent and the probability of success may change from trial to trial.
Bayes's theorem is used to update prior probabilities based on the arrival of new relevant information.
True
Permutations are used when the order in which different objects are arranged matters.
True
The exponential distribution is related to the Poisson distribution.
True
Mutually exclusive and collectively exhaustive events ______________.
contain all outcomes in a sample space and do not share common outcomes.
The standard normal distribution is a normal distribution with a mean equal to zero and a standard deviation equal to one.
true
According to the Department of Transportation, 27% of domestic flights were delayed in 2007 at JFK airport. Five flights are randomly selected at JFK. What is the probability that all five flights are delayed?
0.0014 For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated as formula16.mml Calculate P(X = 5). The Excel's function BINOM.DIST can be used.
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 more than five hours to construct a soapbox derby car.
0.0228 The normal transformation implies that any value x of X has a corresponding value z of Z given by 2formula69.mml Compute P(X > 5).
Forty-four percent of consumers with credit cards carry balances from month to month. Four consumers with credit cards are randomly selected. What is the probability that all consumers carry a credit card balance?
0.0375 For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated as 2formula16.mml Calculate P(X = 4). The Excel's function BINOM.DIST can be used.
Suppose the life of a particular brand of laptop battery is normally distributed with a mean of 8 hours and a standard deviation of 0.6 hours. What is the probability that the battery will last more than 9 hours before running out of power?
0.0475 The normal transformation implies that any value x of X has a corresponding value z of Z given by formula88.mml Compute P(X > 9). Note that P(Z > z) = 1 - P(Z < z).
The odds against winning $1.00 in the lottery are 19 to 1. What is the probability of winning $1.00 in the lottery?
0.05 Given odds against event A occurring of "a to b," the probability of A is b/a+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?
0.0746
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?
0.0746 For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated as 2formula16.mml The Excel's function BINOM.DIST can be used.
Gold miners in Alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1,000 tons of dirt is normally distributed. What is the probability the miners find more than 16 ounces of gold in the next 1,000 tons of dirt excavated?
0.0918 The normal transformation implies that any value x of X has a corresponding value z of Z given by 2formula83.mml Compute P(X > 16). Note that P(Z ≥ z) = 1 - P(Z < z).
Suppose the round-trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between Boston and San Francisco will be less than $300?
0.1020 The normal transformation implies that any value x of X has a corresponding value z of Z given by 1formula147.mml Compute P(X > $450). Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. Compute P(Z > z) = 1 - P(Z ≤ z).
The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States, but even when analysis is restricted to relatively strong housing markets the numbers are staggering. For example, in 2011 an average of three residential properties were auctioned off each weekday in the city of Boston, up from an average of one per week in 2005. What is the probability that exactly four foreclosure auctions occurred on a randomly selected weekday of 2011 in Boston?
0.1680 For a Poisson random variable X, the probability of x successes over a given interval of time or space is calculated as formula19.mmlthe mean number of successes; e ≈ 2.718.
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. Find the missing values marked xx and yy in the following contingency table.
0.1698 The contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table.
Studies have shown that bats can consume an average of 10 mosquitoes per minute. What is the probability that a bat consumes four mosquitoes in a 30-second interval?
0.1755 For a Poisson random variable X, the probability of x successes over a given interval of time or space is calculated as formula19.mmlthe mean number of successes; e ≈ 2.718. Calculate P(X = 4). Time interval is important. The Excel's function POISSON.DIST can be used.
Suppose the round-trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between Boston and San Francisco will be more than $450?
0.1788 The normal transformation implies that any value x of X has a corresponding value z of Z given by 1formula147.mml Compute P(X > $450). Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. Compute P(Z > z) = 1 - P(Z ≤ z).
A bank manager estimates that an average of two customers enter the tellers' queue every five minutes. Assume that the number of customers that enter the tellers' queue is Poisson distributed. What is the probability that exactly three customers enter the queue in a randomly selected five-minute period?
0.1804 For a Poisson random variable X, the probability of x successes over a given interval of time or space is calculated as formula19.mmlthe mean number of successes; e ≈ 2.718. The Excel's function POISSON.DIST can be used.
Given the information in the accompanying table, calculate the correlation coefficient between the returns on Stocks A and B. Stock A Stock B E(RA ) = μA = 8.4% E(RB ) = μB = 6.5% σA = 11.80% σB = 7.29% Cov(RA,RB ) = σAB = 16.70%
0.194 The correlation coefficient between the returns RA and RB is calculated as formula15.mml
Let formula137.mml, and formula138.mml, and formula139.mml. Compute formula140.mml.
0.20 The total probability rule conditional on two events B and Bc is defined as formula136.mml.
The following probability table shows probabilities concerning Favorite Subject and Gender. What is the probability of selecting an individual preferring science if she is female? Gender Favorite Subject Total Math English Science Male 0.200 0.050 0.175 0.425 Female 0.100 0.325 0.150 0.575 Total 0.300 0.375 0.325 1.000
0.2609 The contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table.
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. What is the probability that two of the expectant mothers will have a Caesarean delivery?
0.3088 For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated as2formula16.mml The Excel's function BINOM.DIST can be used.
According to the Mortgage Bankers Association, 8% of U.S. mortgages were delinquent in 2011. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure. A random sample of eight mortgages was selected. What is the probability that exactly one of these mortgages is delinquent?
0.3570 For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated as formula16.mml Calculate P(X = 1). The Excel's function BINOM.DIST can be used.
Mark Zuckerberg, the founder of Facebook, announced that he will eat meat only from animals that he has killed himself (Vanity Fair, November 2011). Suppose 257 people were asked, "Does the idea of killing your own food appeal to you, or not?" The accompanying contingency table, cross-classified by gender, is produced from the 187 respondents. Male Female Yes 35 20 No 56 76 Given that the respondent is male, the probability that he feels that the idea of killing his own food is appealing is the closest to ____.
0.38 A contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table. 35/91 = 0.384
A bank manager estimates that an average of two customers enters the tellers' queue every five minutes. Assume that the number of customers that enters the tellers' queue is Poisson distributed. What is the probability that fewer than two customers enter the queue in a randomly selected five-minute period?
0.4060 For a Poisson random variable X, the probability of x successes over a given interval of time or space is calculated as formula19.mmlthe mean number of successes; e ≈ 2.718. P(X < 2) = P(X = 0) + P(X = 1). The Excel's function POISSON.DIST can be used.
Find the probability P(-1.96 ≤ Z ≤ 0).
0.4750 Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. Compute P(z1 ≤ Z ≤ z2) = P(Z ≤ z2) - P(Z ≤ z1).
Mark Zuckerberg, the founder of Facebook, announced that he will eat meat only from animals that he has killed himself (Vanity Fair, November 2011). Suppose 257 people were asked, "Does the idea of killing your own food appeal to you, or not?" The accompanying contingency table, cross-classified by gender, is produced from the 187 respondents. Male Female Yes 35 20 No 56 76 The probability that a respondent to the survey is male is the closest to ____.
0.49 The contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table.
According to a Department of Labor report, the city of Detroit had a 20% unemployment rate in May of 2011. Eight working-age residents were chosen at random. What is the probability that at least two of the residents were unemployed?
0.4967 For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated asformula16.mml P(X ≥ 2) = 1 - (P(X = 0) + P(X = 1)). The Excel's function BINOM.DIST can be used.
Gold miners in Alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1,000 tons of dirt is normally distributed. What is the probability the miners find between 10 and 14 ounces of gold in the next 1,000 tons of dirt excavated?
0.4972 The normal transformation implies that any value x of X has a corresponding value z of Z given by formula85.mml Compute P(10 ≤ X ≤ 14). Note that P(z1 ≤ Z ≤ z2) = P(Z ≤ z2)1 - P(Z ≤ z1).
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. Under 30 30+ Yes 76 65 No 24 35 The probability that a respondent is at least 30 years old is the closest to ______.
0.50
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. Under 30 30+ Yes 76 65 No 24 35 The probability that a respondent is at least 30 years old is the closest to ______.
0.50 The contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table.
A company is bidding on two projects, A and B. The probability that the company wins project A is 0.40 and the probability that the company wins project B is 0.25. Winning project A and winning project B are independent events. What is the probability that the company wins project A or project B?
0.55 The addition rule is calculated as formula170.mml. P(AuB)=P(A)+P(B)-P(AnB)
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. Chocolate Vanilla Swirl Under 25 years old 40 20 15 At least 25 years old 15 40 20 What is the probability a randomly selected customer prefers swirled yogurt or is at least 25 years old?
0.60 A contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table.
The following table shows the number of students who did not attend statistics class over the 30 class meetings last semester. Number of students Frequency 0 4 1 7 2 9 3 5 4 5 What is the probability that there will be more than one student absent in class today?
0.63 The probability distribution of a discrete random variable is a list of the values with the associated probabilities. Calculate P(X > 1).
A survey of adults who typically work full time from home recorded their current education level. The results are shown in the table below. Education Level Frequency Bachelor's degree or higher 32 Associate degree 12 High school only 4 Less than high school 2 The probability that a randomly selected adult who works full time from home has a bachelor's degree or higher is ______.
0.64
Let formula131.mml, and formula132.mml. Compute formula133.mml. Let P(AnB)=0.3, and P(AnB^c)=0.15, Compute P(B|A)
0.67 The total probability rule conditional on two events B and Bc is defined as formula130.mml. P(A)=P(AnB)+P(AnB^c)=P(A|B)P(B)+P(A|B^c)P(B^c)
The number of cars sold by a car salesperson during each of the last 25 weeks is the following: Number Sold Frequency 0 10 1 10 2 5 What is the standard deviation of the number of cars sold by the salesperson during a week?
0.75 The standard deviation of the discrete random variable X is calculated as formula9.mml The variance of the discrete random variable X is calculated as Var(X) = σ2 = ∑(xi - μ)2 P(X = xi).
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 probability that no more than one of the customers redeems the coupon?
0.7528 For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated asformula16.mml The Excel's function BINOM.DIST can be used.
You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. An inexpensive bag you are considering advertises to be good for temperatures down to 38°F. What is the probability that the bag will not be warm enough?
0.7734 The normal transformation implies that any value x of X has a corresponding value z of Z given by formula81.mml Compute P(X > 38). Note that P(Z ≥ z) = 1 - P(Z < z).
The number of cars sold by a car salesperson during each of the last 25 weeks is the following: Number Sold Frequency 0 10 1 10 2 5 What is the expected number of cars sold by the salesperson during a week?
0.8 The expected value of X is calculated as E(X) = μ = ∑xi P(X = xi).
The number of cars sold by a car salesperson during each of the last 25 weeks is the following: Number Sold Frequency 0 10 1 10 2 5 What is the expected number of cars sold by the salesperson during a week?
0.8 The expected value of X is calculated as E(X) = μ = ∑xi P(X = xi).
You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. One sleeping bag you are considering advertises that it is good for temperatures down to 25°F. What is the probability that this bag will be warm enough on a randomly selected May night at the park?
0.8106 The normal transformation implies that any value x of X has a corresponding value z of Z given by formula79.mml Compute P(X ≥ 25). Note that P(Z ≥ z) = 1 - P(Z < z).
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. What is the probability that at least one of the expectant mothers will have a Caesarean delivery?
0.9394 For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated as formula16.mml P(X ≥ 1) = 1 - P(X = 0). The Excel's function BINOM.DIST can be used.
Find the probability P(-1.96 ≤ Z ≤ 1.96).
0.9500 Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. Compute P(z1 ≤ Z ≤ z2) = P(Z ≤ z2) - P(Z ≤ z1).
The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States, but even when analysis is restricted to relatively strong housing markets the numbers are staggering. For example, in 2011 an average of three residential properties were auctioned off each weekday in the city of Boston, up from an average of one per week in 2005. What is the probability that at least one foreclosure auction occurred in Boston on a randomly selected weekday of 2011?
0.9502 For a Poisson random variable X, the probability of x successes over a given interval of time or space is calculated as 2formula19.mmlthe mean number of successes; e ≈ 2.718. P(X ≥ 1) = 1 - P(X = 0). The Excel's function POISSON.DIST can be used.
The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States, but even when analysis is restricted to relatively strong housing markets the numbers are staggering. For example, in 2011 an average of three residential properties were auctioned off each weekday in the city of Boston, up from an average of one per week in 2005. What is the probability that at least one foreclosure auction occurred in Boston on a randomly selected weekday of 2011?
0.9502 For a Poisson random variable X, the probability of x successes over a given interval of time or space is calculated as 2formula19.mmlthe mean number of successes; e ≈ 2.718. P(X ≥ 1) = 1 - P(X = 0). The Excel's function POISSON.DIST can be used.
Consider the following probability distribution. xi P(X = xi) -2 0.2 -1 0.1 0 0.3 1 0.4 The standard deviation is ____.
1.14 The standard deviation of the discrete random variable X is calculated as formula7.mml The variance of the discrete random variable X is calculated as Var(X) = σ2 = ∑(xi - μ)2 P(X = xi).
The number of homes sold by a realtor during a month has the following probability distribution: Number Sold Probability 0 0.20 1 0.40 2 0.40 What is the expected number of homes sold by the realtor during a month?
1.2 The expected value of X is calculated as E(X) = μ = ∑xi P(X = xi)
Consider the following frequency distribution. Class Frequency 12 up to 15 3 15 up to 18 6 18 up to 21 3 21 up to 24 4 24 up to 27 4 How many observations are less than 21?
12
There are 30 Major League Baseball teams in the National League. Five of these teams will make the playoffs at the end of the season. The number of unique groups of teams that can make the playoffs is ______.
142,506
There are 30 Major League Baseball teams in the National League. Five of these teams will make the playoffs at the end of the season. The number of unique groups of teams that can make the playoffs is ______.
142506
Consider a population with data values of 12 8 28 22 12 30 14. The population mean is ____.
18
Amounts spent by a sample of 200 customers at a retail store are summarized in the following relative frequency distribution. Amount Spent (in $) Frequency 0 up to 10 15 10 up to 20 75 20 up to 30 55 30 up to 40 55 The mean amount spent by customers is the closest to _____.
22.50
An analyst constructed the following frequency distribution on the monthly returns for 50 selected stocks. Class (in percent) Frequency -10 up to 0 8 0 up to 10 25 10 up to 20 15 20 up to 30 2 The number of stocks with returns of 0% up to 10% is ______.
25
How many project teams composed of five students can be created out of a class of 10 students?
252
Let X be normally distributed with mean µ = 250 and standard deviation σ = 80. Find the value x such that P(X ≤ x) = 0.9394.
374 Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. Given probability find z value. The inverse transformation implies that any value z of Z has a corresponding value x of X given by x = μ + zσ.
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% The addition rule is calculated as formula120.mml.
An investor owns a portfolio consisting of two mutual funds, A and B, with 35% invested in A. The following table lists the inputs for these funds. Measure Fund A Fund B Expected Value 10 5 Variance 98 26 Covariance 22 The standard deviation for the portfolio return is ____.
5.74% The standard deviation of the portfolio is formula14.mml The portfolio variance is calculated as formula12.mml
An investor owns a portfolio consisting of two mutual funds, A and B, with 35% invested in A. The following table lists the inputs for these funds. Measure Fund A Fund B Expected Value 10 5 Variance 98 26 Covariance 22 The expected return for the portfolio return is ____.
6.75% An expected return of the portfolio E (Rp) is calculated as E (Rp) = WAE (RA) + WBE (RB); WA and WB are portfolio weights.
An analyst expects that 20% of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company is headed for a decline, there is a 90% chance that this ratio will be negative. If the company is not headed for a decline, there is only a 10% chance that the ratio will be negative. The analyst randomly selects a company with a negative ratio. Based on Bayes's theorem, the posterior probability that the company will experience a decline is
69%
An analyst expects that 20% of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company is headed for a decline, there is a 90% chance that this ratio will be negative. If the company is not headed for a decline, there is only a 10% chance that the ratio will be negative. The analyst randomly selects a company with a negative ratio. Based on Bayes's theorem, the posterior probability that the company will experience a decline is
69% The Bayes's theorem calculates the posterior probability as 2formula147.mml
For any normally distributed random variable with mean μ and standard deviation σ, the percent of the observations that fall between [μ - 2σ, μ + 2σ] is the closest to _______.
95.44% The empirical rule states that P(μ - 2σ ≤ X ≤ μ + 2σ) = 0.9544.
Given that the probability distribution is normal, it is completely described by its mean μ > 0 and its standard deviation σ > 0.
A normal distribution is completely characterized by its mean and standard deviation, but while the standard deviation is always positive, the mean of the normally distributed random variables can be positive or negative.
Which of the following represents a subjective probability?
A skier believes she has a 10% chance of winning a gold medal. For well-defined problems an a priori probability can be calculated by reasoning about the problem.
What is probability?
A value between 0 and 1 assigned to an event that measures the likelihood of its occurrence. A probability is a numeric value, between zero and one, that measures the likelihood that an uncertain event occurs.
The cumulative distribution function is denoted and defined as which of the following?
F(x) and F(x) = P(X ≤ x)
Combinations are used when the order in which different objects are arranged matters.
False
The total probability rule is defined as P(A) = P(A 2formula10.mml B) P(A2formula10.mmlformula11.mml)
False
A probability distribution of a continuous random variable X gives the probability that X takes on a particular value x, P(X = x).
False If X is a continuous random variable, then P(X = x) = 0 for any value x.
The probability density function for a continuous uniform distribution is positive for all values between -∞ and +∞.
False The uniform distribution is defined on a bounded interval, denoted by [a, b].
A Bernoulli process consists of a series of n independent and identical trials of an experiment such that in each trial there are three possible outcomes and the probabilities of each outcome remain the same.
False A Bernoulli process consists of a series of n independent and identical trials of an experiment such that in each trial there are only two possible outcomes (success and failure), and in each trial the probability of a success (and failure) remains the same.
Just as in the case of the continuous uniform distribution, the probability density function of the normal distribution may be easily used to compute probabilities.
False As opposed to the simple probability density function, f(x) = formula17.mml, for the uniform distribution, the density function for the normal distribution is f(x) = formula18.mml This function is very difficult to handle because the areas under this function cannot be found using standard calculus. However, the z table and Excel's function NORM.DIST can be used to approximate these areas.
Given that the probability distribution is normal, it is completely described by its mean μ > 0 and its standard deviation σ > 0.
False A normal distribution is completely characterized by its mean and standard deviation, but while the standard deviation is always positive, the mean of the normally distributed random variables can be positive or negative.
Joint probability of two independent events A and B equals the sum of the individual probabilities of A and B.
False For independent events, the joint probability equals: P(AnB) = P(A) P(B).
The mean and standard deviation of the continuous uniform distribution are equal.
False The mean or the expected value of X for the continuous uniform distribution is computed as 1formula9.mml, where a and b are lower and upper limits of values. The standard deviation of X is computed as 1formula10.mml
A standard normal variable Z can be transformed to the normally distributed random variable X with only mean µ known.
False To transform the standard normal variable Z to the normally distributed random variable X we need to know the mean and standard deviation: X = µ + Zσ.
An marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and collects monthly data for 25 firms. He estimates the model: Sales = β0 +β1 Advertising + ε. The following ANOVA table below shows a portion of the regression results. df SS MS F Regression 1 78.53 78.53 3.58 Residual 23 504.02 21.91 Total 24 582.55 Coefficients Standard Error t-stat p-value Intercept 40.1 14.08 2.848 0.0052 Advertising 2.88 1.52 -1.895 0.0608 Which of the following is true?
If Advertising goes up by $100, then on average, Sales go up by $2,880. In the simple linear regression model the coefficient b1 measures the change in the predicted value of the response variable formula209.mml given a unit increases in the associated explanatory variable. Estimate the change.
Which of the following sets of outcomes described below in I and II represent mutually exclusive events? I. "Your final course grade is an A"; "Your final course grade is a B." II. "Your final course grade is an A"; "Your final course grade is a Pass."
Only I represents mutually exclusive events. Events are mutually exclusive if they do not share any common outcome of a random experiment.
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(AuB)=0.52
If A and B are independent events, which of the following is correct?
P(A|B)=P(A)
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). The normal distribution is symmetric around its mean: P(X < μ) = P(X > μ) = 0.5. If x < μ then P(X < x) < 0.5 and P(X < μ) > P(X < x).
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 normal distribution is symmetric around its mean: P(X < μ) = P(X > μ) = 0.5. If x < μ then P(X < x) < 0.5 and P(X > x) > 0.5.
Testing whether the computer is infected or not would be best described using binomial probability distribution.
True A binomial random variable is defined as the number of successes achieved in the n trials of a Bernoully process.
The probability density function of a continuous random variable is the counterpart to the probability mass function of a discrete random variable.
True The area under any probability density function is 1, and as for any discrete random variable X with values x1, x2, x3, . . . , xn, formula152.mml.
The number of syntactic errors found in a program code would best be described using a Poisson probability distribution.
True The random experiment satisfies a Poisson process if the number of successes within a specified time or space interval equals any integer between zero and infinity.
Bayes's theorem is used to update prior probabilities based on the arrival of new relevant information.
True Bayes's theorem is a procedure for updating probabilities based on new information.
The intersection of two events A and B, denoted by Aformula1.mmlB, is the event consisting of all outcomes that are in A and B.
True The intersection of two events is the event consisting of all outcomes in A and B.
The exponential distribution is related to the Poisson distribution.
True the exponential distribution is related to the Poisson distribution even though the Poisson distribution deals with discrete random variables.
Mutually exclusive and collectively exhaustive events ______________.
contain all outcomes in a sample space and do not share common outcomes. Events are mutually exclusive if they do not share any common outcome of a random experiment. Events are collectively exhaustive if all possible outcomes of a random experiment are included in the events.
The intersection of events A and B, denoted by formula55.mml, ___________.
contains outcomes that are both in A and B.
A survey of adults who typically work full time from home recorded their current education level. The results are shown in the table below. Education Level Frequency Bachelor's degree or higher 32 Associate degree 12 High school only 4 Less than high school 2 Calculating the probability that a randomly selected adult who works full time from home has an associate degree is using ________ probability.
empirical Relative frequencies are used to calculate the empirical probability of event.
After extensive research, an analyst asserts that there is an 80% chance that ABC Corporation will beat its EPS forecast. Analogously, the odds for the company beating its EPS forecast are _______.
four to one The odds for A occurring equal is formula67.mml, and the odds against A occurring is formula68.mml
Find the missing values marked xx and yy in the following contingency table. Age Group Preferred Form of Exercise Total Running Biking Swimming Under 35 years 157 121 yy 357 35 years or older 45 xx 87 159 Total 202 148 166 516
xx = 27, yy = 79 The contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table.
Find the z value such that P(Z ≤ z) = 0.9082.
z=1.33
Which of the following is not an event when considering the sample space of tossing two coins?
{HH, TT, HTH} Check the number of coins tossed in the sample space
The intersection of events A = {apple pie, peach pie, pumpkin pie} and B = {cherry pie, blueberry pie, pumpkin pie} is ____________.
{pumpkin pie} The intersection of two events, formula58.mml, is the event consisting of all outcomes in A and B.