**MATH 221 Statistics for Decision Making ****Week 4 Homework **

MATH 221 Statistics for Decision Making Week 4 Homework

Question 1The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.54 minutes and a standard deviation of 1.91. Find the probability that a randomly selected individual will take less than 6 minutes to select a shoe purchase. Is this outcome unusual?

Probability is 0.09, which is unusual as it is less than 5%

Probability is 0.91, which is usual as it is greater than 5%

Probability is 0.09, which is usual as it is not less than 5%

Probability is 0.91, which is unusual as it is greater than 5%

Question 2Monthly water bills for a city have a mean of $108.43 and a standard deviation of $36.98. Find the probability that a randomly selected bill will have an amount greater than $165, which the city believes might indicate that someone is wasting water. Would a bill that size be considered unusual?

Probability is 0.06, which is unusual as it is not less than 5%

Probability is 0.06, which is usual as it is not less than 5%

Probability is 0.94, which is usual as it is greater than 5%

Probability is 0.94, which is unusual as it is greater than 5%

Question 3In 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.

0.40

Less than 1%

0.70

0.30

Question 4A 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 0.70mm. Would this outcome warrant a refund (meaning that it would be unusual)?

Probability of 0.79 and would not warrant a refund

Probability of 0.79 and would warrant a refund

Probability of 0.21 and would not warrant a refund

Probability of 0.21 and would warrant a refund

Question 5A grocery stores studies how long it takes customers to get through the speed check lane. They assume that if it takes more than 10 minutes, the customer will be upset. Find the probability that a randomly selected customer takes more than 10 minutes if the average is 7.45 minutes with a standard deviation of 2.81 minutes.

0.818

0.636

0.182

0.018

Question 6In 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 1100 acres, about how many would be expected to yield more than 190 bushels of corn per acre?

503 acres

419 acres

461 acres

639 acres

Question 7On average, the parts from a supplier have a mean of 31.8 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 27.0 and 36.6 inches. Is this consistent with the Empirical Rule of 68%-95%-99.7%?

Probability is 0.95, which is consistent with the Empirical Rule

Probability is 0.02, which is inconsistent with the Empirical Rule

Probability is 0.98, which is inconsistent with the Empirical Rule

Probability is 0.95, which is inconsistent with the Empirical Rule

Question 8A process is normally distributed with a mean of 10.6 hits per minute and a standard deviation of 0.49 hits. If a randomly selected minute has 11.8 hits, would the process be considered in control or out of control?

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

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

Question 9The candy produced by a company has a sugar level that is normally distributed with a mean of 16.1 grams and a standard deviation of 0.9 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, 19.4. Is the process in control or out of control and why?

It is out of control as two of these data points are more than 2 standard deviations from the mean

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

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 out of control as one of these data points is more than 3 standard deviations from the mean

Question 10The 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, what warranty should be provided so that the company is replacing at most 5% of their toasters sold?

5.9 years

7.3 years

4.6 years

4.3 years

**APA Writing Checklist**

Use this document as a checklist for each paper you will write throughout your GCU graduate

program. Follow specific instructions indicated in the assignment and use this checklist to help ensure correct grammar and APA formatting. Refer to the APA resources available in the GCU Library and Student Success Center.

Check Out Also:** MATH 221 Statistics for Decision Making Week 5 Homework **

☐ APA paper template (located in the Student Success Center/Writing Center) is utilized for the correct format of the paper. APA style is applied, and format is correct throughout.

☐ The title page is present. APA format is applied correctly. There are no errors.

☐ The introduction is present. APA format is applied correctly. There are no errors.

☐ Topic is well defined.

☐ Strong thesis statement is included in the introduction of the paper.

☐ The thesis statement is consistently threaded throughout the paper and included in the conclusion.

☐ Paragraph development: Each paragraph has an introductory statement, two or three sentences as the body of the paragraph, and a transition sentence to facilitate the flow of information. The sections of the main body are organized to reflect the main points of the author. APA format is applied correctly. There are no errors.

☐ All sources are cited. APA style and format are correctly applied and are free from error.

☐ Sources are completely and correctly documented on a References page, as appropriate to assignment and APA style, and format is free of error.

**Scholarly Resources: **Scholarly resources are written with a focus on a specific subject discipline and usually written by an expert in the same subject field. Scholarly resources are written for an academic audience.

**Examples of Scholarly Resources include:** Academic journals, books written by experts in a field, and formally published encyclopedias and dictionaries.

**Peer-Reviewed Journals:** Peer-reviewed journals are evaluated prior to publication by experts in the journal’s subject discipline. This process ensures that the articles published within the journal are academically rigorous and meet the required expectations of an article in that subject discipline.

**Empirical Journal Article**: This type of scholarly resource is a subset of scholarly articles that reports the original finding of an observational or experimental research study. Common aspects found within an empirical article include: literature review, methodology, results, and discussion.

Adapted from “Evaluating Resources: Defining Scholarly Resources,” located in *Research Guides* in the GCU Library.

☐ The writer is clearly in command of standard, written, academic English. Utilize writing resources such as Grammarly, LopesWrite report, and ThinkingStorm to check your writing.