IS 310 Exam 2

From a group of six people, two individuals are to be selected at random. How many possible pairs elections are possible? a.15 b.8 c.12 d.36

a.15

For the standard normal probability distribution, what is the z-score, z0, For an upper-tail probability of .025? (i.e., Find z such that P(Z >z0)=.025.) a.1.65 b.-1.96 c.1.96 D.-2.33

b.-1.96

For a normal probability distribution,The area to the right of the mean is given by a.1.00 b.3.09 c.1.96 d.0.50

d.0.50

For any continuous random variable X with mean = μ and STD = σ,the probability That X = μ is ... a.50% b.0.5 c.0.15 D.0

D.0

For the standard normal probability distribution, what is the z-value, z0,corresponding to an upperone-tail probability of 0.5 (i.e., p (Z > z0) = 0.5)? a.1.65 b.1.96 c.2.33 D.0

D.0

For any Discrete random variable X, the probability X assumes any value between a and b, (i.e., P(a< X < b))is equal to the area under probability density function, f(x),between a and b.

FALSE

One major difference between the counting rule for combinations and the counting rule for permutations is that with combinations, order of selection is important.

FALSE

Probabilities for any random variable, regardless of what values its mean and STD equal ,can be Found by converting to z-scores and using the standard normal cumulative probability table.

FALSE

The standard deviations of all normal random variables must equal one.

FALSE

A probability near 0 indicates that an event or outcome is likely to occur.

False

For a Discrete random variable X, with the set of outcomes equal to the set of non-Negative even integers = (0, 2, 4, 6, 8,10...),the probability that X assumes any Value Between and including 2 but strictly less than 10, P(2 ≤ X < 10)is given by... P(2 ≤ X <10) = P(X=2) + P(X=4)+P(X=6)+ P(X=8)+P(X=10).

False

.A random variable with Poisson distribution is an example of a continuous random Variable.

TRUE

A random variable that Describes the number of customers that enter a store is an example of a Continuous random variable.

TRUE

Empirical discrete probability distribution functions assign probabilities to outcomes of a random variable that are equivalent to their relative frequencies.

TRUE

For a Discrete random variable X, the sum of probabilities across all possible outcomes must equal one.

TRUE

For any normal random variable X with mean =0 and STD=σ, P(X <−σ) =P(X>σ).

TRUE

Let X be the grade a student earns in Business Statistics, where X =A, B, C, D or F. Then X is an example of a discrete random variable.

TRUE

Probabilities for A normally distributed random variable may be calculated by first transforming the observed data value to its z-score and using the standard normal cumulative probability distribution table (Aka "the Standard Normal table").

TRUE

Probability is a numerical measure between 0 and 1 quantifying the likelihood that an event or particular outcome will occur.

TRUE

The PDF for all Continuous random variables must be greater than or equal to zero and less than or equal to one.

TRUE

Two required conditions for a discrete Uniform probability function, pdf, f(x) are 1) f(x) must be non-Negative and 2) sum of f(x) across all possible outcomes of the Random Variable equals 1.

TRUE

For a Continuous random variable X, the probability that X = x for a<x<b is given By f(b)−f(a), where f(a) and f(b) are the probability density function evaluated at the endpoints x=a and x=b, respectively.

TRUE Probabilities for a specific value are 0

One assumption of the binomial probability distribution function, f(x), is that the probability for X Successes must be the same for all x.

TRUE, the probability of success for any number of outcomes must be the same for binomial probability distribution

For a Continuous random variable X, P(X ≤ a) = P(X <a) for any real number, a.

TRUE; Because the standard normal random variable is continuous and continuous random variables exist in intervals instead of specific values, so there is no difference between "less than" and "less than or equal to"

Consider a binomial experiment with n=10 and p=.3. Compute the probability that X=0? a. 0 b. 0.7^ 10 c. 0.3 ^10 d. 0.7^0= 1

b. 0.7^ 10

Let X be a random variable equal to the number of IS 310 students that ace the second midterm. Suppose previous data suggests that the probability that a student aces the second midterm is 0.1. If there are 40 students taking the exam, how many students do you predict will aces the test? a. 0 b. 4 c. 3.5 d. 36

b. 4

For the r.v. Z with the standard normal probability distribution,what is the probability associated with -1.00 ≤z≤ 1.00? a.0.3432 b.0.6827 c.0.8413 D.0.1587

b.0.6827

For the standard normal random variable Z, what probability is associated with The area underneath the PDF Between z=−1.96and 1.96? a.0.90 b.0.95 c.0.99 D.0.99

b.0.95

.For the standard normal probability distribution, What z-value, z0,corresponds to P(Z >z0) =.95? a.1.96 b.1.65 c.-1.65 D.-1.96

b.1.65

14. For normal distributions which of the following is NOT True regarding the probability density function (pdf), f(x)? a.As the standard deviation increases, the graph of the pdf, f(x), flattens and becomes wider. b.As the mean increases, so does central location of the pdf, f(x). c.As the standard deviation decreases, the graph of the pdf, f(x), narrows And Becomes taller. d.As both the mean and the standard deviation increase,the graph of the pdf becomes skewed to the right.

b.As the mean increases, so does central location of the pdf, f(x).

A discrete probability distribution for which all possible outcome values are equally likely is known as the a.Empirical probability distribution. b.Discrete uniform probability distribution. c.Binomial probability distribution. d.Poisson probability distribution.

b.Discrete uniform probability distribution.

Which of the following is NOT a property of a discrete probability distribution function, f(x)? a.f(x)>0 for all Possible outcomes b.If x < 0 then f(x) =0 c.f(x) ≤ 1 d.∑f(x)=1 for all possible outcomes

b.If x < 0 then f(x) =0

For a random variable X distributed uniformly on the interval [−2,−4],which of the following is true about the pdf for X, f(x)? a.f(x)=−2 for −4<x<−2. b.f(x) = −0.5 for −4<x<−2. c.f(x) = 0.5 for −4<x<−2. d.f(x) is undefined for x < 0.

b.f(x) = −0.5 for −4<x<−2.

For a continuous random variable X,The Value of the probability density function At X=a, where "a"Is a positive real number, is a.0 b.greater than 0. c.less than 0 d.a cat.

b.greater than 0.

In the standard normal distribution, the a.mean and the standard deviation are both 1. b.mean is 0 and the standard deviation is 1. c.mean is 0 and the standard deviation can have any value greater than 0. d.mean is "really mean" and the standard deviation is "a true deviant."

b.mean is 0 and the standard deviation is 1.

For a normal random variable, X, with mean = 4 and STD =2, what is the Probability that the outcome of the r.v. is less than −2 (i.e., P(X < −2))? a.-0.5. b.0.5 c.0.001 D.−0.0011

c.0.001

4. A CSULB study reported That last year 95% of gym members Who signed up for"P91-Extreme Workout" quit before the course was over. What probability distribution would you use to calculate the probability that exactly 5 of the 30 gym members enrolled in P91 will quit?(Hint:You have all of the information that you need to compute the probability.) a.Empirical probability distribution. b.Discrete uniform probability distribution. c.Binomial probability distribution. d.Poisson probability distribution.

c.Binomial probability distribution.

"Talkaholism" is an accepted measure of individuals' level of talkativeness. Assume that the probability distribution is unimodal and symmetrical (like a bell). What probability distribution would you use to calculate the probability that the average talkativeness score among students sitting in the back Of Dr. Ritter's IS310 class has a standardized "z-score" of 3 or higher(i.e., talk waaaay too much)?(Hint: You have all of the information you need to compute the probability). a. Uniform Probability Distribution b. Normal Probability distribution c.Discrete Normal probability distribution d. Continuous binomial probability Distribution

c.Discrete Normal probability distribution

."Argumentativeness" refers to students' propensity or willingness to confront or argue with others (they actually enjoy arguing). Assume that the probability distribution is unimodal and symmetrical (like a bell). What probability distribution would you use to calculate the probability that the Standardized Argumentativeness z-score among A students is between 2.5 and 3? (Hint: You have all of the information you need to compute the probability). a. Uniform probability distribution b. Normal Probability distribution c.Discrete Normal probability distribution d. Continuous binomial probability distribution

c.Discrete Normal probability distribution

Which of the following is NOT A Continuous random variable? a.X=time it takes a person to eat ('er,I mean"bake")one pound of Mrs.Field's cookie dough b.X=distance a person runs to work off all of the cookies he/she "baked." c.X=color of baggy clothes to make a person look thinner. 10d.X= weight gain for each pound of cookie dough that a person "bakes."

c.X=color of baggy clothes to make a person look thinner.

The standard deviation of a normal distribution a.must be between−3 and 3. b.is always 1. c.can be any positive value. d.Is negative.

c.can be any positive value.

A negative value for a z-score indicates that a.a mistake has been made in computations, since z cannot be negative. b.the original observation is to the right or above the mean. c.the original observation is to the left or below the mean. d.the data have a negative attitude.

c.the original observation is to the left or below the mean.

Consider a normally distribution random Variable X,with mean=10 and STD = 5. Compute the probability that X=15. a. 0 b.0.68 c.−0.84 d. 0.84

d. 0.84

Which of the following PDFs has the property that the probability That a continuous r.v.assumes a value in an interval ,is the same as the probability that The r.v. assumes a value in any other interval ,provided that the two intervals are of equal length, for all intervals contained in the outcome space? a. Uniform Probability distribution b. Normal probability distribution c.Binomial probability distribution d. Poisson probability distribution

d. Poisson probability distribution

NCAA estimates that the Average yearly value of a full athletic scholarship at in-state public universities like CSULB is $19,000 (WSJ, March 12, 2012). Assume the Yearly Athletic scholarship value is normally distributed with a STD of $2,100. For a scholarship of $17,758, what must be true about its z-score? a. 1 <z-score< 24 b.z-score =0 c.-1 <z-score<0 d.0 <z-score< 1

d.0 <z-score< 1

More than 50 million guests stay at bed and breakfasts (B&Bs) each year. The website for the Bed and Breakfast Inns of North America averages five visitors per minute and enables many B&Bs to attract guests. What probability distribution would you use to estimate the probability That the website has 17 or more visitors in the next three-minute period? (Hint:You have all of the information that you need to compute the probability.) a.Empirical probability distribution. b.Discrete uniform probability distribution. c.Binomial probability distribution. d.Poisson probability distribution.

d.Poisson probability distribution.

Which one of these variables is a continuous random variable? a.X=amount of mercury found in fish caught in the Gulf of Mexico (in mg3/kg2) b.X= 0 if "male," X=1 if "female," X=2 if "other" or "decline to state" c.X=number of cars filled with 35 gallons of gasoline. d.X=grains of sand on the beaches of Southern California.

d.X=grains of sand on the beaches of Southern California.

The highest point of a normal curve occurs at a.two standard deviations to the right of the mean b.the top of Mt. Everest. c.one standard deviation to the right of the mean. d.the mean.

d.the mean.

For standard normal random variable Z, P(Z <−1) = P(Z> 1)

True

Apple introduced a smaller variant of the Apple iPad weighing less than 11 oz. The "mini" is about 50% lighter than the standard iPad. Battery tests for the mini showed that the probability of the battery life within any 1-minute interval is the same as that Within any other 1-minute contained within the larger interval of possible battery life (8 to 12 hours). What probability distribution would you use to calculate the probability that the battery life of the new mini is between 9 and 10 hours? (Hint: You have all of the information you need to compute the probability). a. Uniform Probability distribution b. Normal Probability distribution c.Discrete Uniform probability distribution d.Poisson probability distribution

a. Uniform Probability distribution

You are interested in bidding on a house and we know that there is another interested bidder. The seller announced that the highest bid in excess of $300K will be accepted. We know that the competitor's bid is between $300K and $350K. Assume that the probability of bid within any $5K interval is the same as the probability of a bid within any other $5K interval contained in the larger interval from $300K to $350K. What probability distribution would you recommend to determine the probability that your bid of less than $325K will be accepted? (Hint: You have all of the information you need to compute the probability). a. Uniform probability distribution b. Normal Probability distribution c.Discrete Uniform probability Distribution d. Empirical probability Distribution

a. Uniform probability distribution

Which one of these variables is a discrete random variable? a. X=number of pizza slices eaten by a student. b.X=time it takes a pizzeria to deliver a pizza. c.X=Weight of pizza eaten by a student (measured in ounces). d. X=weight of a student after eating a pizza (in pounds)

a. X=number of pizza slices eaten by a student.

.Out of a cauldron of 50 Snicker bars, 80 Reece's peanut butter cups, and 20 Almond Joys, what probability distribution would you use to calculate the probability of Selecting a Snicker bar.(Hint: You have all of the information that you need to compute the probability.) a.Empirical probability distribution. b.Discrete uniform probability distribution. c.Binomial probability distribution. d.Poisson probability distribution.

a.Empirical probability distribution.