MATH 221 Week 3 Quiz

MATH 221 Week 3 Quiz | Devry University

Week 3: Homework

 Question 1

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

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

·         Continuous  

·         Discrete  

·         Lagging  

·         Nonsensical

 

 Question 2

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

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

·         Distributed  

·         Inferential  

·         Continuous    

·         Discrete

 

 Question 3

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 30-39?

Homework Help:

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

·         18.9%  

·         42.5%  

·         23.7% 

·         16.5%

 

 Question 4

Consider 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.

________________________________________

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

3DC. Mean or expected value of discrete variables (Links to an external site.) (DOCX)  

·         40.7  

·         39.5  

·         40.0  

·         39.0

 

 Question 5

Consider the following table.

Defects in batch               Probability

0              0.37

1              0.24

2              0.16

3              0.09

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)

3DG. Variance and Standard Deviation of discrete variables (Links to an external site.) (DOCX)  

·         1.50  

·         2.50  

·         1.43  

·         2.25

 

Question 6

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.

________________________________________

Homework Help:

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

3DG. Variance and Standard Deviation of discrete variables (Links to an external site.) (DOCX) 

·         3.48    

·         1.51  

·         2.27  

·         4.50

 

 Question 7

Ten fourth graders are randomly selected. The random variable represents the number of fourth graders who own a smartphone. 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 selected is the same for all fourth graders    

·         The probability of owning a smartphone is the same for all fourth graders  

·         All ten selected fourth graders are the same age  

·         The probability of being a fourth grader is the same for all those selected

 

 Question 8

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?

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

·         0.07    

·         7  

·         x, the counter  

·         0.31

 

Question 9

Fifty-nine percent of US adults have little confidence in their cars. You randomly select eight US adults. Find the probability that the number of US adults who have little confidence in their cars is (1) exactly three and then find the probability that it is (2) more than 6.

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)  

·         0.133 (2) 0.096  

·         0.904 (2) 0.974  

·         0.133 (2) 0.904  

·         0.199 (2) 0.096

 

 Question 10

Eleven baseballs are randomly selected from the production line to see if their stitching is straight. Over time, the company has found that 98.3% of all their baseballs have straight stitching. If exactly nine of the eleven have straight stitching, should the company stop the production line?

3VC. Binomial probabilities and distributions (Links to an external site.) (1:49)  

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

·         Yes, the probability of exactly nine having straight stitching is unusual  

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

·         No, the probability of nine or more having straight stitching is not unusual

 

 Question 11

A 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?

3VE. Binomial experiments (Links to an external site.) (3:26)

3DI. Examples of binomial and non-binomial experiments (Links to an external site.) (DOCX)  

·         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  

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

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

 

 Question 12

In a box of 12 tape measures, there is one that does not work. Employees take a tape measure as needed. The tape measures are not returned, once taken. You are the 8th employee to take a tape measure. Is this a binomial experiment?

3VE. Binomial experiments (Links to an external site.) (3:26)

3DI. Examples of binomial and non-binomial experiments (Links to an external site.) (DOCX) 

·         Yes, the probability of success is one out of 12 with 8 selected  

·         No, the probability of getting the broken tape measure changes as there is no replacement  

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

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

 

 

Question 13

Fifty-three percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 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?

3VC. Binomial probabilities and distributions (Links to an external site.) (1:49)  

·         0, 1, 7, 8    

·         0, 1, 2, 8  

·         1, 2, 7, 8  

·         1, 2, 8

 

 Question 14

The probability of a potential employee passing a drug test is 91%. If you selected 15 potential employees and gave them a drug test, how many would you expect to pass the test?

3VD. Mean, variance, and standard deviation for binomial experiments (Links to an external site.)

3DH. Mean, Variance, and Standard Deviation of a binomial variable (Links to an external site.) (DOCX)  

·         12 employees  

·         13 employees  

·         14 employees  

·         15 employees

 

 Question 15

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?

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

3DH. Mean, Variance, and Standard Deviation of a binomial variable (Links to an external site.) (DOCX)  

·         0.975  

·         0.768  

·         0.916  

·         0.037