# Math 221 – quizzes – week 3 homework

Question 1 2 pts

Let x represent the number of pets in pet stores. This would be considered what type of variable:

Discrete

Nonsensical

Continuous

Lagging

Question 2 2 pts

Let x represent sheets of paper in a package. This would be considered what type of variable:

Distributed

Continuous

Inferential

Discrete

Question 3 2 pts

Consider the following table.

Age Group Frequency

18-29           9831

30-39           7845

40-49           6869

50-59           6323

60-69           5410

70 and over 5279

If you created the probability distribution for these data, what would be the probability of 40-49?

16.5%

18.9%

23.7%

42.5%

Question 4 2 pts

Consider the following table.

Weekly hours   worked    Probability

1-30   (average=22)              0.08

31-40   (average=35)            0.16

41-50   (average=46)            0.72

51 and over   (average=61)  0.04

Find the mean of this variable.

39.0

40.2

35.9

41.0

Question 5 2 pts

Consider the following table.

Defects in   batch      Probability

0                                   0.28

1                                   0.35

2                                   0.16

3                                   0.09

4                                   0.10

5                                   0.02

Find the variance of this variable.

1.44

0.85

1.35

1.83

Question 6 2 pts

Consider the following table.

Defects in   batch      Probability

2                                 0.35

3                                 0.23

4                                 0.20

5                                 0.09

6                                 0.07

7                                 0.06

Find the standard deviation of this variable.

1.51

2.27

4.50

3.48

Question 7 2 pts

The standard deviation of the number of video game A’s outcomes is 05479, while the standard deviation of the number of video game B’s outcomes is 0.2498. Which game would you be likely to choose if you wanted players to have the most choice and why?

Game A, as   the standard deviation is higher and, thus offers fewer choices in outcomes

Game B, as   the standard deviation is lower and, thus offers more choices in outcomes

Game A, as   the standard deviation is lower and, thus offers fewer choices in outcomes

Game B, as   the standard deviation is higher and, thus offers more choices in outcomes

Question 8 2 pts

Thirty-five percent of teens buy soda (pop) at least once each week. Eleven kids are randomly selected. The random variable represents the number of these kids who purchase soda (pop) at least once each week. For this to be a binomial experiment, what assumption needs to be made?

The probability of being a teen and being a kid should be the same.

All teens have the same probability of being selected.

All the kids eligible to be selected are teens.

All eleven kids selected live in the same region.

Question 9 2 pts

A survey found that 31% of all teens buy soda (pop) at least once each week. Seven teens are randomly selected. The random variable represents the number of teens who buy soda (pop) at least once each week. What is the value of n?

x, the counter

0.07

0.31

7

Question 10 2 pts

Forty-four percent of US adults have little confidence in their cars. You randomly select twelve US adults. Find the probability that the number of US adults who have little confidence in their cars is (1) exactly six and then find the probability that it is (2) more than 7.

(1) 0.793 (2)   0.0099

(1) 0.207 (2)   0.901

(1) 0.762 (2)   0.901

(1) 0.207 (2)   0.099

Question 11 2 pts

Say a business wants to know if each salesperson is equally likely to make a sale. The company chooses 5 salespeople and gathers information on their sales experiences. What assumption must be made for this study’s probability results to be used in future binomial experiments?

That for every 5 salespeople, the probability of making a sale is the same

That the probability of each salesperson being one of the selected 5 is the same

That 5% is the correct probability to use in future studies

That the selected 5 have similar characteristics and sales areas as the other   salespeople

Question 12 2 pts

Eight baseballs are randomly selected from the production line to see if their stitching is straight. Over time, the company has found that 93.8% of all their baseballs have straight stitching. If exactly six of the eight have straight stitching, should the company stop the production line?

Yes, the   probability of six or less having straight stitching is unusual

No, the   probability of six or less having straight stitching is not unusual

No, the   probability of exactly six have straight stitching is not unusual

Yes, the   probability of exactly six having straight stitching is unusual

Question 13 2 pts

A soup company puts 20 ounces of soup in each can. The company has determined that 97% of cans have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 24 cans has all cans that are properly filled?

n=20, p=0.97,   x=20

n=24, p=0.97,   x=1

n=24, p=0.97,   x=24

n=20, p=0.97,   x=20

Question 14 2 pts

A supplier must create metal rods that are 18.1 inches width to fit into the next step of production. Can a binomial experiment be used to determine the probability that the rods are the correct width or an incorrect width?

No, as the   probability of being about right could be different for each rod selected

Yes, all   production line quality questions are answered with binomial experiments

No, as there   are three possible outcomes, rather than two possible outcomes

Yes, as each   rod measured would have two outcomes: correct or incorrect

Question 15 2 pts

In a box of 12 pens, there is one that does not work. Employees take pens as needed. The pens are returned once employees are done with them. You are the 5th employee to take a pen. Is this a binomial experiment?

No, binomial does not include systematic selection such as “fifth”

No, the probability of getting the broken pen changes as there is no replacement

Yes, you are find the probability of exactly 5 not being broken

Yes, with replacement, the probability of getting the one that does not work is the   same

Question 16 2 pts

Forty-two percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 7 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?

1, 6, 7

1, 2, 6, 7

0, 6, 7

0, 1, 2, 7

Question 17 2 pts

Eighty-one percent of products come off the line within product specifications. Your quality control department selects 15 products randomly from the line each hour. Looking at the binomial distribution, if fewer than how many are within specifications would require that the production line be shut down (unusual) and repaired?

Fewer than 12

Fewer than 9

Fewer than 11

Fewer than 10

Question 18 2 pts

The probability of a potential employee passing a drug test is 86%. If you selected 12 potential employees and gave them a drug test, how many would you expect to pass the test?

8 employees

9 employees

10 employees

11 employees

Question 19 2 pts

The probability of a potential employee passing a training course is 86%. If you selected 15 potential employees and gave them the training course, what is the probability that more than 12 will pass the test?

0.852

0.900

0.648

0.352

Question 20 2 pts

Off the production line, there is a 3.7% chance that a candle is defective. If the company selected 45 candles off the line, what is the probability that fewer than 3 would be defective?

0.768

0.975

0.918

0.037