true/false questions - Answers
A probability near 0 indicates that an event or outcome is likely to occur. - Answers False
For a Discrete random variable X, the sum of probabilities across all possible outcomes must equal
one. - Answers 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.
- Answers TRUE
Probabilities for a specific value are 0
For standard normal random variable Z, P(Z <−1) = P(Z> 1) - Answers True
For a Continuous random variable X,
P(X ≤ a) = P(X <a) for any real number, a. - Answers 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"
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). - Answers False
Probability is a numerical measure between 0 and 1 quantifying the likelihood that an event or
particular outcome will occur. - Answers TRUE
One assumption of the binomial probability distribution function, f(x), is that the probability for X
Successes must be the same for all x. - Answers TRUE,
the probability of success for any number of outcomes must be the same for binomial probability
distribution
One major difference between the counting rule for combinations and the counting rule for
permutations is that with combinations, order of selection is important. - Answers FALSE
The PDF for all Continuous random variables must be greater than or equal to zero and less than or
equal to one. - Answers TRUE
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. - Answers FALSE
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"). - Answers TRUE
For any normal random variable X with mean =0 and STD=σ, P(X <−σ) =P(X>σ). - Answers TRUE
The standard deviations of all normal random variables must equal one. - Answers FALSE
A random variable that Describes the number of customers that enter a store is an
example of a Continuous random variable. - Answers TRUE
.A random variable with Poisson distribution is an example of a continuous random
Variable. - Answers TRUE
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. - Answers
FALSE
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. - Answers
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. - Answers TRUE
Empirical discrete probability distribution functions assign probabilities to outcomes of a random
variable that are equivalent to their relative frequencies. - Answers TRUE
Multiple Choice Chapters 4 &5 - Answers
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. - Answers 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 - Answers b.If x < 0 then f(x) =0
.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. - Answers a.Empirical probability distribution.
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. - Answers c.Binomial probability distribution.
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. - Answers 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 - Answers d.0 <z-score< 1
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 - Answers a.15
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) - Answers a. X=number of pizza slices eaten
by a student.
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. - Answers d.X=grains of sand on the
beaches of Southern California.
Consider a binomial experiment with n=10 and p=.3.