Module 5 Prelims & Final Quiz

Select all variables which represent discrete random variables? (you will need to mark more than one item)

A. the area of a randomly select classroom on campus, reported in square feet

B. the number of babies born at a hospital in a 24 hour period

C. the temperature of a beverage served at a restaurant

D. the number of children at an elementary school who take medications daily

B. the number of babies born at a hospital in a 24 hour period

D. the number of children at an elementary school who take medications daily

X	0	1	2	3	4
P(X)	0.31	0.24	0.19	0.15	0.11

For the given probability distribution, find the probability that X is 2 or 3.

0.34

For the given probability distribution, what is the  probability X is at most 2?

X	0	1	2	3	4	5
P(X)	0.10	0.14	0.17	0.25	0.22	0.12

0.41

P(at most 2) = P(2 or less) = P(2, 1, or 0) = 0.17 + 0.14 + 0.10 = 0.41

Find the expected value (mean) of this probability distribution.

X	0	1	2	3	4
P(X)	0.3	0.2	0.2	0.15	0.15

A. 2.05

B. 2.0

C. 1.75

D. 1.65

D. 1.65

Find the standard deviation of this probability distribution.

X	0	1	2	3	4
P(X)	0.3	0.2	0.2	0.15	0.15

A. 1.424

B. 2.03

C. 0.86

D. 1.65

A. 1.424

What is the shape of this probability distribution.

X	0	1	2	3	4
P(X)	0.3	0.25	0.2	0.15	0.1

A. skewed right

B. skewed left

C. uniform

D. symmetric and bell shaped

A. skewed right

The probability distribution is missing three of the probabilities.  Regardless, find the probability X is at least 5.  

x           2       3        4        5       6       7     8     9  

P(x)    .05    .08     .16     .23    .20      ?      ?      ?

A. 0.48

B. 0.21

C. 0.52

D. 0.71

D. 0.71

Two ways to tell if an event is rare or uncommon are...

A. if the probability is greater than 0.05

B. if the probability is less than 0.05

C. if all of the outcomes in the event are two or more standard deviations away from the mean

D. if the outcomes in the event are all two or fewer standard deviations away from the mean

B. if the probability is less than 0.05

C. if all of the outcomes in the event are two or more standard deviations away from the mean

A probability distribution has a mean of 5.45 and a standard deviation of 1.88.

Is the event "X is less than or equal to one" a rare event or not?

Determine this using the mean and standard deviation.

A. yes, the event is more than two standard deviations from the mean

B. no, the event is less than two standard deviations from the mean

C. yes, the event is less than two standard deviations from the mean

D. no, the event is more than two standard deviations from the mean

A. yes, the event is more than two standard deviations from the mean

The probability distribution for X is provided.

Is the event "X is at least 7" a rare event or not? 

x       1     2      3       4      5     6      7      8

P(x)  .03  .12   .24   .26   .17   .10   .06   .02

A. No, the probability of the event is less than 0.05

B. No, the probability of the event is greater than 0.05

C. Yes, the probability of the event is less than 0.05

D. Yes, the probability of the event is greater than 0.05

B. No, the probability of the event is greater than 0.05

Which of the following is not a requirement for distribution to be considered a binomial distribution?

A. the number of desired successes must be larger than 2

B. the probability of a success must remain constant across all trials

C. independent trials

D. each trial must result in either a success or a failure

A. the number of desired successes must be larger than 2

Suppose it is known that 9.1% of Florida residents are left eye dominant.  If a random sample of 55 Florida residents is selected, how many left eye dominant  residents do we expect to find?  

Round your answer to two decimal places if needed. 

5.01

Suppose it is known that 11.0% of Georgia residents are left handed when it comes to throwing a ball.   A random sample of 45 Georgia residents is selected.  What is the standard deviation of the number of Georgia residents in the sample who are left handed throwers?

Round your answer to two decimal places if needed. 

2.10

Suppose it is known that 38% of Facebook users are over the age of 60.  A random sample of 120 Facebook users is selected.  Let X represent the number in the sample who are over the age of 60.  What value is two standard deviations above the mean?

Round your answer to two decimal places.

56.23

It is known that every person has a 40% chance of making an impulse purchase at a specific grocery store. If 10 customers are randomly selected, what is the probability that exactly 3 make an impulse purchase at that grocery store?   

Round your answer to three decimal places  (e.g. if your answer is 0.02473, you would enter 0.025)

0.215

It is known that 66% of the people in a large city are in favor of a newly proposed law.  If 10 people from this city are randomly selected, what is the probability that exactly 7 of them are in favor of the newly proposed law?

Round your answer to three decimal places (e.g. an answer of 0.259113 would round to 0.259)

0.257

At a large university, 57% of the students frequently visit the university's cafeteria.  If 15 students are randomly selected, what is the probability that exactly 11 frequently visit the cafeteria?   

Round your answer to 3 decimal places.

(0.096)

At a large university, 20% of the students frequently visit the university's library.  If 15 students are randomly selected, what is the probability that 3 or fewer frequently visit the library?   

Round your answer to 3 decimal places. 

0.648

It is known that 34% of the people who make a purchase from a Coca-Cola vending machine get a low calorie beverage.  If 9 people purchase a beverage from a Coca-Cola vending machine, what is  the probability that less than 3 of them order a low calorie beverage? 

Round your answer to 3 decimal places. 

0.363

At a gas station, it is known that 75% of the individuals stopping at the store will purchase fuel.   If a random sample of 8 people stopping at the store is selected, what is the probability that 6 or more of them will purchase fuel?

Round your answer to two decimal places

0.68

X	0	1	2	3	4
P(X)	0.31	0.24	0.19	0.15	0.11

For the given probability distribution, find the probability that X is 2 or 3.

0.34

sum the probabilities under X = 2 and X = 3

Outcomes in a probability distribution are mutually exlcusive

The event of a customer buying a dairy product at a grocery store can be modeled after a binomial distribution where the probabilty of a customer buying a dariy product is 0.40.  If 20 cusomers at the grocery store are randomly selected, what is the expected value (mean) of the number of customers who will buy a dairy product?   Do not round your answer.  

Answer:

8

The mean or expected value for a binomial distribution in n*p

An person randomly selects five universities in the state of Georgia. Let the random variable X be the number of these universities selected that have two or more campuses. The possible values of X are ...

A. 2, 3, 4 or larger

B. 0, 1, 2

C. 1, 2, 3, 4, 5

D. 0, 1, 2, 3, 4, 5

D. 0, 1, 2, 3, 4, 5

X is the number of universities out of the five that have the two or more campuses.  It could turn out that none of those  selected have the two or more campues..... up to all five have the multiple campuses.

Determine which one of the following binomial distributions will provide a symmetric bell shape. (Recall the two requirements for a binomial distribution to be symmetric and bell shaped.)

A. Z is binomial with n = 100 and p = 0.04

B. X is binomial with n = 50 and p = 0.1

C. W is binomial with n = 20 and p = 0.8

D. Y is binomial with n = 30 and p = 0.5

D. Y is binomial with n = 30 and p = 0.5

In order to insure the desired symmetric bell shape, both n*p and n*(1-p) must be at least 10

Each of the following variables are either discrete or continuous. Select all of the discrete variables.

A. amount of time a car waits in a drive-thru lane

B. number of items ordered at a drive thru window

C. weight of items stored in a storage unit

B. number of items ordered at a drive thru window

discrete variables are countable.  Weight and time are both meausured not counted

The probability distribution, where X can be equal to integers 2 through 7,  is missing two of the probabilities.  Regardless, find the probability X is at most 4.  

x           2         3           4         5           6         7      

P(x)       ?          ?         0.15     0.24     0.20      0.14 

0.42

"At most four" means "four or less".  Since the distribution's probabilities must sum to one, we can subtract the probabilities of 5, 6 and 7 from one to get our desired answer.

If a pair of dice is rolled, the probability the sum of the two dice will be nine is approximately 0.1111.   If a person rolls a pair of dice  8 times, what is  the probability they get a sum of nine on exactly  2 of the 8 rolls? 

Round your answer to 3 decimal places. 

0.171

This is binomial with n = 8, p = 0.1111, X = 2

For the given probability distribution, what is the  probability X is at most 2?

X	1	2	3	4	5	6
P(X)	0.20	0.24	0.17	0.15	0.12	0.12

0.44

It is known that 28% of the people who make a purchase from a Coca-Cola vending machine get a low calorie beverage.  If 9 people purchase a beverage from a Coca-Cola vending machine, what is  the probability that less than 3 of them order a low calorie beverage? 

Round your answer to 3 decimal places.

0.517

Since we want the probability of less than three (three is not included) we are looking to find  P(X < 2).  This problem contains all of the attributes of a binomial distribution so using the Binomial CDF with n = 9, p = proportion who buy low calorie drinks, and X = 2, will proivde the correct answer. 

Remember, binomial CDF sums all probabilities less than or equal to the value of X provided.