Exp 7

Suppose that you are an elementary school teacher and you are evaluating the reading levels of your students. You find an individual that reads 57.4 word per minute. You do some research and determine that the reading rates for their grade level are normally distributed with a mean of 100 words per minute and a standard deviation of 24 words per minute.

a. At what percentile is the child’s reading level (round final answer to one decimal place).

b. Create a graph with a normal curve that illustrates the problem.

For the graph do NOT make an empirical rule graph, just include the mean and the mark off the area that corresponds to the student’s percentile. There is a Normal Distribution Graph generator linked in the resources area. Upload file containing your graph below. Question 1 Part 2 of 3Choose FileNo file chosen

c. Make an argument to the parents of the child for the need for remediation. Structure your essay as follows:

1. A basic explanation of the normal distribution
2. Why the normal distribution might apply to this situation
3. Describe the specific normal distribution for this situation (give the mean and standard deviation)
4. Interpret the answer to part a. including a definition of percentile.
5. Explain how the graph created in part b. represents the child’s reading level.
6. Use the answers to parts a. and b. to emphasize the gravity of the situation.
7. Give a suggested course of action.

Suppose that you are working for a chain restaurant and wish to design a promotion to disabuse the public of notions that the service is slow. You decide to institute a policy that any customer that waits too long will receive their meal for free. You know that the wait times for customers are normally distributed with a mean of 16 minutes and a standard deviation of 3 minutes. Use statistics to decide the maximum wait time you would advertise to customers so that you only give away free meals to at most 0.5% of the customers.

a. Determine an estimate of an advertised maximum wait time so that 0.5% of the customers would receive a free meal. Round to one decimal place. minutes

b. Include a graph illustrating the solution. For the graph do NOT make an empirical rule graph, just include the mean and the mark off the area that corresponds to the 0.5% who would receive the refund. There is a Normal Distribution Graph generator linked in the resources area. Combine the above into as single file and upload using the link below. Question 2 Part 2 of 3Choose FileNo file chosen

c. Write a response to the vice president explaining your prescribed maximum wait time. Structure your essay as follows:

1. An advanced explanation of the normal distribution
2. Why the normal distribution might apply to this situation
3. Describe the specific normal distribution for this situation (give the mean and standard deviation)
4. Explain how the graph created in part b. represents the waiting times of the customers.
5. Explain the answer to part a. in terms of both the customers who get a free meal and those who do not. Feel free to use the accurate answer in part a to determine a “nice” wait time to be used in the actual advertising campaign.
6. Use the answers to parts a. and b. to explain how the proposal will not result in a loss of profit for the company.

Exp 8 Application

The amount of contaminants that are allowed in food products is determined by the FDA (Food and Drug Administration). Common contaminants in cow milk include feces, blood, hormones, and antibiotics. Suppose you work for the FDA and are told that the current amount of somatic cells (common name “pus”) in 1 cc of cow milk is currently 750,000 (note: this is the actual allowed amount in the US!). You are also told the standard deviation is 77000 cells. The FDA then tasks you with checking to see if this is accurate.

You collect a random sample of 50 specimens (1 cc each) which results in a sample mean of 765990 pus cells. Use this sample data to create a sampling distribution. Assume that the population mean is equal to the FDA’s legal limit and see what the probability is for getting your random sample.

a. Why is the sampling distribution approximately normal?

b. What is the mean of the sampling distribution?

c. What is the standard deviation of the sampling distribution?

d. Assuming that the population mean is 750,000, what is the probability that a simple random sample of 50 1 cc specimens has a mean of at least 765990 pus cells?

e. Is this unusual? Use the rule of thumb that events with probability less than 5% are considered unusual.

• No
• Yes

f. Explain your results above and use them to make an argument that the assumed population mean is incorrect. (6 points) Structure your essay as follows:

1. Describe the population and parameter for this situation.
2. Describe the sample and statistic for this situation.
3. Give a brief explanation of what a sampling distribution is.
4. Describe the sampling distribution for this situation.
5. Explain why the Central Limit Theorem applies in this situation.
6. Interpret the answer to part d.
7. Use the answer to part e. to argue that the assumed population mean is either correct or incorrect. If incorrect, indicate whether you think the actual population mean is greater or less than the assumed value.
8. Explain what the FDA should do with this information.