Math

Week 4: Homework

Started: Apr 24 at 9:59am

Quiz Instructions

 

Be sure to complete the Active Reading assignment before the Homework.

The Active Reading assignment is worth points and will help your understanding of the material.

1. Click the button to start the homework set. 

2. You can re-do this assignment as often as you need.

Be sure to have the Week 4 Excel spreadsheet available to help with the calculations. It is provided in  Week 4: Resources .

Also - Don't be concerned if you notice that Canvas calls this assignment a "quiz". Quiz is the assignment category it uses whenever an assignment uses the format of questions and answers.  This is actually your  Homework assignment, which is separate from the weekly Quiz and this Homework should be done prior to the Quiz.

Recommended Sequence

In addition to the discussions:

1. Active Reading assignment

2. Homework

3. Quiz

Get Started

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Top of Form

 

Flag question: Question 1

Question 12 pts

The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.21 minutes and a standard deviation of 1.90. Find the probability that a randomly selected individual will take less than 6 minutes to select a shoe purchase. Is this outcome unusual?

Homework Help:

4VA. Calculating normal probabilities  (2:18)

4DF. Probabilities from Normal DistributionsLinks to an external site.  (DOCX)

Group of answer choices

Probability is 0.12, which is unusual as it is less than 5%

Probability is 0.12, which is usual as it is not less than 5%

Probability is 0.88, which is unusual as it is greater than 5%

Probability is 0.88, which is usual as it is greater than 5%

 

Flag question: Question 2

Question 22 pts

In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally distributed variable. Find the probability that randomly selected individual would spent between 30 and 40 minutes on the treadmill.

Homework Help:

4VA. Calculating normal probabilities  (2:18)

4DF. Probabilities from Normal DistributionsLinks to an external site.  (DOCX)

Group of answer choices

0.40

0.70

0.30

Less than 1%

 

Flag question: Question 3

Question 32 pts

A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.98mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.50mm. Would this outcome warrant a refund (meaning that it would be unusual)?

Homework Help:

4VA. Calculating normal probabilities (Links to an external site.)  (2:18)

4DA. Description of normal distribution, area, and probabilities, definition of unusual events (Links to an external site.) (DOCX)

Group of answer choices

Probability of 0.09 and would warrant a refund

Probability of 0.91 and would not warrant a refund

Probability of 0.09 and would not warrant a refund

Probability of 0.91 and would warrant a refund

 

Flag question: Question 4

Question 42 pts

In an agricultural study, the average amount of corn yield is normally distributed with a mean of 185.2 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study included 1200 acres, about how many would be expected to yield more than 190 bushels of corn per acre?

Homework Help:

4VB. Calculating number from a sample that meet criteria based on normal probabilitiesLinks to an external site.  (1:32)

Group of answer choices

419 acres

503 acres

581 acres

282 acres

 

Flag question: Question 5

Question 52 pts

On average, the parts from a supplier have a mean of 35.8 inches and a standard deviation of 2.4 inches. Find the probability that a randomly selected part from this supplier will have a value between 31.0 and 40.6 inches. Use the Empirical Rule of 68%-95%-99.7%.

Homework Help:

4DB. Connection between normal probabilities and Empirical RuleLinks to an external site.  (DOCX)

Group of answer choices

Probability is 0.05

Probability is 0.95

Probability is 0.02

Probability is 0.98

 

Flag question: Question 6

Question 62 pts

In a normally distributed data set a mean of 31 where 99.7% of the data fall between 16.6 and 45.4, what would be the standard deviation of that data set?

Homework Help:

4VG. Empirical Rule with examplesLinks to an external site.  (4:38)

4DE. Standard scores and the Empirical RuleLinks to an external site.  (DOCX)

Group of answer choices

8.4

9.6

7.6

4.8

 

Flag question: Question 7

Question 72 pts

In a normally distributed data set with a mean of 24 and a standard deviation of 4.2, what percentage of the data would be between 19.8 and 28.2 and why?

Homework Help:

4VG. Empirical Rule with examplesLinks to an external site.  (4:38)

4DE. Standard scores and the Empirical RuleLinks to an external site.  (DOCX)

Group of answer choices

95% based on the Empirical Rule

68% based on the histogram

95% based on the histogram

68% based on the Empirical Rule

 

Flag question: Question 8

Question 82 pts

A process is normally distributed with a mean of 10.2 hits per minute and a standard deviation of 1.04 hits. If a randomly selected minute has 13.9 hits, would the process be considered in control or out of control?  Use a control chart to answer the question.

Homework Help:

4VC. Calculating probabilities from manufacturing to determine if system is in control (Links to an external site.)  (4:12)

Group of answer choices

Out of control as this one data point is more than three standard deviations from the mean

Out of control as this one data point is more than two standard deviations from the mean

In control as this one data point is not more than three standard deviations from the mean

In control as only one data point would be outside the allowable range

 

Flag question: Question 9

Question 92 pts

The candy produced by a company has a sugar level that is normally distributed with a mean of 16.8 grams and a standard deviation of 0.7 grams. The company takes readings of every 10th bar off the production line. The reading points are 17.3, 14.9, 18.3, 16.5, 16.1, 17.4, 18.4. Is the process in control or out of control and why?  Use a control chart to answer the question.

Homework Help:

4VC. Calculating probabilities from manufacturing to determine if system is in control (Links to an external site.)  (4:12)

Group of answer choices

It is out of control as at least two of three consecutive data points are more than 2 standard deviations from the mean

It is in control as at least two of three consecutive data points are more than 2 standard deviations from the mean

It is in control as none of these data points is more than 3 standard deviations from the mean

It is out of control as the values jump above and below the mean

 

Flag question: Question 10

Question 102 pts

The toasters produced by a company have a normally distributed life span with a mean of 5.8 years and a standard deviation of 0.9 years, the company is willing to have a warranty that replaces at most 10% of their toasters sold.  What is the longest a blender can last and still be in the lowest 10% of life spans?

Homework Help:

4VD. Calculating probabilities to compare to set probabilities such as warranties and production guidelines (Links to an external site.)  (2:23)

Group of answer choices

4.5 years

4.6 years

4.3 years

5.9 years

 

Flag question: Question 11

Question 112 pts

A running shoe company wants to sponsor the fastest 3% of runners. You know that in this race, the running times are normally distributed with a mean of 7.2 minutes and a standard deviation of 0.56 minutes. How fast would you need to run to be sponsored by the company?

Homework Help:

4VD. Calculating probabilities to compare to set probabilities such as warranties and production guidelines (Links to an external site.)  (2:23)

Group of answer choices

8.1 minutes

8.3 minutes

6.1 minutes

6.3 minutes

 

Flag question: Question 12

Question 122 pts

A stock’s price fluctuations are approximately normally distributed with a mean of $29.51 and a standard deviation of $3.87. You decide to sell whenever the price reaches its highest 10% of values. What is the highest value you would still hold the stock?

Homework Help:

4VE. Determining values from normal distributions based on probabilitiesLinks to an external site.  (2:42)

4DC. Using normal distributions and probabilities to determine set valuesLinks to an external site.  (DOCX)

Group of answer choices

$30.00

$34.47

$24.55

$33.38

 

Flag question: Question 13

Question 132 pts

Hospital waiting room times are normally distributed with a mean of 38.12 minutes and a standard deviation of 8.63 minutes. What is the shortest wait time that would still be in the longest 20% of wait times?

Homework Help:

4VE. Determining values from normal distributions based on probabilities (Links to an external site.)  (2:42)

4DC. Using normal distributions and probabilities to determine set values  DOCX

Group of answer choices

30.86 minutes

27.06 minutes

49.18 minutes

45.38 minutes

 

Flag question: Question 14

Question 142 pts

The length of timber cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.52 inches. In a random sample of 45 boards, what is the probability that the mean of the sample will be between 94.5 inches and 95.1 inches?

Homework Help:

4VF. Calculating probabilities using the Central Limit Theorem (Links to an external site.)  (4:32)

4DD. Central Limit Theorem, definition of unusual events  DOCX

Group of answer choices

0.009

0.408

0.591

0.901

 

Flag question: Question 15

Question 152 pts

Of all the companies on the New York Stock Exchange, profits are normally distributed with a mean of $6.54 million and a standard deviation of $10.45 million. In a random sample of 73 companies from the NYSE, what is the probability that the mean profit for the sample was between 3.0 million and 6.0 million?

Homework Help:

4VF. Calculating probabilities using the Central Limit Theorem (Links to an external site.)  (4:32)

4DD. Central Limit Theorem, definition of unusual events  DOCX

Group of answer choices

0.215

0.328

0.325

0.015