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A fair, six-sided number cube has the numbers 2, 2, 4, 4, 6, 6 on its faces. Sarah rolls this number cube 10 times and records the number of times a 2 is rolled.Have the conditions for a binomial setting been met for this scenario?

A
Yes, all four conditions in BINS have been met.
B
No, the rolls of a number cube are not independent of one another.
C
No, this is not a fair number cube because each outcome shows on more than one face.
D
No, without any odd-numbered faces, we cannot determine the probability of rolling a 2.
2
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At a carnival game, the chance of winning a prize is 0.45. Kylee plays the game 3 times. Using the table, what is the probability that she wins at most 2 prizes?

Question illustration
A
0.09
B
0.33
C
0.58
D
0.91
3

The owner of a local movie theater keeps track of the number of tickets sold in each purchase and makes a probability distribution based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table.

Question illustration
A
2
B
2.1
C
2.5
D
3
4

Renee and Thomas live at the beach and collect seashells. The number of shells Renee collects on any given day, R, is approximately Normal with a mean of 58.2 shells and a standard deviation of 12.8 shells. The number of shells Thomas collects on any given day, T, is approximately Normal with a mean of 47.9 shells and a standard deviation of 11.5 shells. Assume the two random variables are independent of each other.What is the probability that on a randomly selected day the total number of shells collected by Renee and Thomas is 120 or more?

A
0.002
B
0.209
C
0.284
D
0.791
5

Based upon historical data, it is known that 8% of 12-egg cartons contain at least one broken egg. A grocery store manager would like to carry out a simulation to estimate the number of cartons, in a sample of 10, that would contain at least one broken egg. She assigns the digits to the outcomes:01-08 = carton contains a broken egg09-99, 00 = carton does not contain a broken eggHere is a portion of a random number table.In the first trial, line 1, one of the first 10 double-digit numbers is between 01 and 08, meaning that 1 of the 10 cartons of eggs contains at least one broken egg. Starting at line 2 and using a new line for each trial, carry out 4 more trials. In what proportion of these 5 trials is there no carton with broken eggs?

Question illustration
A
0
B
0.2
C
0.4
D
0.6
6

At a certain pizzeria, it is known that 12% of orders are for extra-large pizzas. What is the probability that the 6th pizza ordered is the first extra-large pizza?

A
0.0633
B
0.4644
C
0.5277
D
0.9367
7

A medical device company knows that the percentage of patients experiencing injection-site reactions with the current needle is 11%. What is the standard deviation of X, the number of patients seen until an injection-site reaction occurs?

A
3.1289
B
8.5763
C
9.0909
D
11
8

Let A represent the battery life of a brand A laptop, and let B represent the battery life of a brand B laptop. The mean difference in battery life between these two brands of laptops, D = A – B, is –3.25 hours. What is the correct interpretation of this value?

A
On average, brand B gains 3.25 hours of battery life daily.
B
On average, brand A loses 3.25 hours of battery life daily.
C
Both brands are typically losing 3.25 hours of battery life daily.
D
On average, brand B’s battery life lasts 3.25 hours longer than brand A.
9

The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table.

Question illustration
A
A histogram titled Movie tickets has x = number of tickets sold on the x-axis, and probability on the y-axis. 1, 0.55; 2, 0.20; 3, 0.17; 4, 0.06; 5, 0.02.
Option A
B
A histogram titled Movie tickets has x = number of tickets sold on the x-axis, and probability on the y-axis. 1, 0.02; 2, 0.17; 3, 0.20; 4, 0.55; 5, 0.06.
Option B
C
A histogram titled Movie tickets has x = number of tickets sold on the x-axis, and probability on the y-axis. 1, 0.17; 2, 0.55; 3, 0.20; 4, 0.06; 5, 0.02.
Option C
D
A histogram titled Movie tickets has x = number of tickets sold on the x-axis, and probability on the y-axis. 1, 0.02; 2, 0.17; 3, 0.55; 4, 0.20; 5, 0.06.
Option D
10

A commuter train is late to a station 5% of the time. Last week, the train was late on 2 of the 7 days. If the train being late can be considered a random event, what is the probability that the train would be late 2 times in 7 days?

A
0.004
B
0.014
C
0.041
D
0.050
11

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let A represent the score on a randomly selected exam for subject A and let B represent the score on a randomly selected exam for subject B. The distributions of scores for each subject’s standardized tests are displayed in the table and the histograms.

Question illustration
A
Both distributions are roughly unimodal symmetric.
B
Subject A’s distribution is skewed right and subject B’s distribution is skewed left.
C
Subject A’s distribution is roughly unimodal symmetric and subject B’s distribution is skewed left.
D
Subject A’s distribution is roughly unimodal symmetric and subject B’s distribution is skewed right.
12

A local charity holds a carnival to raise money. In one activity, participants make a $3 donation for a chance to spin a wheel that has 10 spaces with the values, 0, 1, 2, 5, and 10. Whatever space it lands on, the participant wins that value. Let X represent the value of a random spin. The distribution is given in the table.

Question illustration
A
The probability of a random spin having a value of at most 5 is 0.8.
B
The probability of a random spin having a value of at least 5 is 0.2.
C
The probability of a random spin having a value lower than 5 is 0.8.
D
The probability of a random spin having a value higher than 5 is 0.1.
13

Based upon historical data, it is known that 8% of 12-egg cartons contain at least one broken egg. A grocery store manager would like to carry out a simulation to estimate the number of cartons, in a sample of 10, that would contain at least one broken egg. She assigns the digits to the outcomes:01-08 = carton contains a broken egg09-99, 00 = carton does not contain a broken eggHere is a portion of a random number table.Beginning at line 1, carry out one trial of this simulation. Use additional lines as needed. How many cartons in this random sample of 10 cartons contain at least one broken egg?

Question illustration
A
0
B
1
C
2
D
3
14

A large hotel has five elevators. On any given day, there is an 8% chance that one elevator is broken The elevators operate independently of one another. The Robertsons are staying in this hotel for five days. Let X represent the number of days one elevator is broken during their stay. What are the mean and standard deviation of X?

A
Mu Subscript x Baseline = 0.4, Sigma Subscript x Baseline = 0.074
Option A
B
Mu Subscript x Baseline = 0.4, Sigma Subscript x Baseline = 0.61
Option B
C
Mu Subscript x Baseline = 2.5, Sigma Subscript x Baseline = 1.92
Option C
D
Mu Subscript x Baseline = 4, Sigma Subscript x Baseline = 0.89
Option D
15

At a carnival game, the chance of winning a prize is 0.45. Elijah plays the game 5 times. What is the probability that he wins 1 prize in 5 games?

A
0.04
B
0.05
C
0.21
D
0.45
16

There are 16 students in a science class. Let X represent the number of students born on a Tuesday. Assuming birthdays in this class are independent of one another, what are the mean and standard deviation of X?

A
Mu Subscript x Baseline = 2.29, Sigma Subscript x Baseline = 1.40
Option A
B
Mu Subscript x Baseline = 3, Sigma Subscript x Baseline = 1.96
Option B
C
Mu Subscript x Baseline = 7, Sigma Subscript x Baseline = 1.51
Option C
D
Mu Subscript x Baseline = 13.71, Sigma Subscript x Baseline = 3.84
Option D
17

A placekicker for a football team makes field goals 55% of the time when kicking from the 35-yard line. Assume that field goal attempts can be considered random events. Using the table, what is the probability that the placekicker will make at least 3 of his next 5 attempts from the 35-yard line?

Question illustration
A
0.34
B
0.26
C
0.60
D
0.74
18

A jar contains 11 red marbles, 12 blue marbles, and 6 white marbles. Four marbles from this jar are selected, with each marble being replaced after each selection. What is the probability that the first red marble chosen is on the 5th selection?

A
0.0128
B
0.0563
C
0.1484
D
0.2815
19

A shipping company claims that 95% of packages are delivered on time. A student wants to conduct a simulation to estimate the number of packages that would need to be randomly selected to find a package that was not delivered on time. The student assigns the digits to the outcomes.00-04 = package not delivered on time05-99 = package delivered on timeHere is a portion of a random number table.Beginning at line 1, and starting each new trial right after the previous trial, carry out 5 trials of this simulation. Based on the 5 trials, what proportion of the time can the shipping company expect to select more than 2 packages before finding one that was not delivered on time?

Question illustration
A
0
B
0.2
C
0.4
D
0.6
20

Hannah has a chicken coop with six hens. Let X represent the total number of eggs the hens lay on a random day. The distribution for X is displayed in the histogram.

Question illustration
A
skewed left
B
skewed right
C
uniform, symmetric
D
approximately Normal

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