# MATH221 Week 3 Homework (July 2019)

MATH 221 Statistics for Decision Making

Week 3 Homework

Question 1Let x represent the number of pets in pet stores. This would be considered what type of variable:

Homework Help:

3DA. Discrete versus continuous variables (Links to an external site.) (DOCX)

Discrete

Nonsensical

Lagging

Continuous

Question 2Let x represent the height of corn in Oklahoma. This would be considered what type of variable:

Homework Help:

3DA. Discrete versus continuous variables (Links to an external site.) (DOCX)

Distributed

Discrete

Continuous

Inferential

Question 3Consider 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?

Homework Help:

3DB. Probabilities from a probability distribution (Links to an external site.) (DOCX)

42.5%

23.7%

18.9%

16.5%

Question 4Consider the following table.

Weekly hours worked Probability

1-30 (average=23) 0.08

31-40 (average=36) 0.16

41-50 (average=43) 0.72

51 and over (average=54) 0.04

Find the mean of this variable.

Homework Help:

3VA. Calculating the mean, variance, and standard deviation of discrete variables (Links to an external site.) (4:35)

3DC. Mean, expected value, variance, and standard deviation of discrete variables (Links to an external site.) (DOCX)

39.0

40.7

39.5

40.0

Question 5Consider the following table.

Defects in batch Probability

0 0.09

1 0.24

2 0.41

3 0.12

4 0.10

5 0.04

Find the variance of this variable.

Homework Help:

3VA. Calculating the mean, variance, and standard deviation of discrete variables (Links to an external site.) (4:35)

3DC. Mean, expected value, variance, and standard deviation of discrete variables (Links to an external site.) (DOCX)

1.48

1.43

1.22

2.02

Question 6Consider the following table.

Defects in batch Probability

2 0.18

3 0.29

4 0.18

5 0.14

6 0.11

7 0.10

Find the standard deviation of this variable.

Homework Help:

3VA. Calculating the mean, variance, and standard deviation of discrete variables (Links to an external site.) (4:35)

3DC. Mean, expected value, variance, and standard deviation of discrete variables (Links to an external site.) (DOCX)

2.49

1.52

4.01

1.58

Question 7The standard deviation of samples from supplier A is 0.0841, while the standard deviation of samples from supplier B is 0.0926. Which supplier would you be likely to choose based on these data and why?

Homework Help:

3DD. Interpreting and comparing discrete variable standard deviations (Links to an external site.) (DOCX)

Supplier B, as their standard deviation is higher and, thus, easier to fit into our production line

Supplier B, as their standard deviation is lower and, thus, easier to fit into our production line

Supplier A, as their standard deviation is lower and, thus, easier to fit into our production line

Supplier A, as their standard deviation is higher and, thus easier to fit into our production line

Question 8Ten frequent gamers are randomly selected. The random variable represents the number of frequent gamers who play video games on their smartphones. For this to be a binomial experiment, what assumption needs to be made?

Homework Help:

3DE. Definitions, assumptions and elements (n, x, p) of binomial experiments (Links to an external site.) (DOCX)

The probability of being a gamer and is selected is the same for all gamers

The probability of being selected is the same for all ten gamers

The probability of being a gamer that plays video games on their smartphones is the same for all gamers

All ten selected gamers are the same age

Question 9A survey found that 75% of all golfers play golf on the weekend. Eighteen golfers are randomly selected. The random variable represents the number of golfers that play on the weekends. What is the value of p?

Homework Help:

3DE. Definitions, assumptions and elements (n, x, p) of binomial experiments (Links to an external site.) (DOCX)

75

0.75

0.18

x, the counter

Question 10Forty-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.

Homework Help:

3VB. Calculating binomial probabilities and cumulative probabilities (Links to an external site.) (8:23)

3DF. Binomial probabilities versus cumulative probabilities (Links to an external site.) (DOCX)

(1) 0.207 (2) 0.901

(1) 0.762 (2) 0.901

(1) 0.793 (2) 0.099

(1) 0.207 (2) 0.099

Question 11Say a business found that 45% of customers in Detroit, MI prefer green sweaters. The company chooses 8 customers in Austin, TX and asks them if they prefer green sweaters. What assumption must be made for this study to follow the probabilities of a binomial experiment?

Homework Help:

3DE. Definitions, assumptions and elements (n, x, p) of binomial experiments (Links to an external site.) (DOCX)

That the probabilities of preferring green sweaters is the same in both cities

That the probability of being a selected customer is the same in both cities

That there is a 45% probability of being a selected customer in either city

That the probability of preferring green sweaters is the same as preferring sweaters from Austin

Question 12Seven baseballs are randomly selected from the production line to see if their stitching is straight. Over time, the company has found that 89.4% of all their baseballs have straight stitching. If exactly five of the seven have straight stitching, should the company stop the production line?

Homework Help:

3VC. Using binomials to assess quality of production (Links to an external site.) (3:08)

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

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

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

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

Question 13A bottling company puts 16 ounces of water bottle in each bottle. The company has determined that 94% of bottles have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 12 cans has all cans that are properly filled?

Homework Help:

3DE. Definitions, assumptions and elements (n, x, p) of binomial experiments (Links to an external site.) (DOCX)

n=16, p=0.94, x=12

n=12, p=0.94, x=12

n=12, p=0.16, x=1

n=12, p=0.98, x=97

Question 14A supplier must create metal rods that are 2.3 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?

Homework Help:

3VC. Using binomials to assess quality of production (Links to an external site.) (3:08)

3DE. Definitions, assumptions and elements (n, x, p) of binomial experiments. (DOCX)

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

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

Question 15In 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?

Homework Help:

3VC. Using binomials to assess quality of production (Links to an external site.) (3:08)

3DE. Definitions, assumptions and elements (n, x, p) of binomial experiments. (DOCX)

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

No, binomial does not include systematic selection such as â€œfifthâ€

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

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

Question 16Eighty-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?

Homework Help:

3VD. Finding unusual outcomes from a probability distribution (Links to an external site.) (2:32)

1, 2, 3, 4

0, 1, 2, 7

1, 2, 3

0, 1, 2, 3

Question 17Sixty-eight 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?

Homework Help:

3VD. Finding unusual outcomes from a probability distribution (Links to an external site.) (2:32)

Fewer than 9

Fewer than 8

Fewer than 10

Fewer than 11

Question 18The 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?

Homework Help:

3DC. Mean, expected value, variance, and standard deviation of discrete variables (Links to an external site.) (DOCX)

9 employees

8 employees

11 employees

10 employees

Question 19The 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?

Homework Help:

3VB. Calculating binomial probabilities and cumulative probabilities (Links to an external site.) (8:23)

0.648

0.852

0.900

0.352

Question 20Off the production line, there is a 4.6% chance that a candle is defective. If the company selected 50 candles off the line, what is the standard deviation of the number of defective candles in the group?

Homework Help:

3VA. Calculating the mean, variance, and standard deviation of discrete variables (Links to an external site.) (4:35)

2.30

1.10

1.48

2.19