E6 Assignment

Suppose the systolic blood pressure (in mm) of adult males has an approximately normal distribution with mean μ =125 and standard deviation σ =14.

Create an empirical rule graph with the following:

• A title and label for the horizontal axis including units.
• Vertical lines for the mean and first 3 standard deviations in each direction with numerical labels on the horizontal axis
• Labels for the areas of the 8 regions separated by the vertical lines as well.

Note: This may be hand drawn or computer generated. See the models for desired formats.

a. Upload your completed file below. Question 1 Part 1 of 5Choose FileNo file chosen

Now use your graph to answer the following questions.

b. About 68% of men will have blood pressure between what amounts?

and

c. What percentage of men will have a systolic blood pressure outside the range 111 mm to 153 mm?

d. Suppose you are a health practitioner and an adult male patient has systolic blood pressure of 171 mm. Use statistics to explain the gravity of his situation. Write an essay below that includes the following:

1. A brief description 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. A brief description of the empirical rule
5. What region of the graph (drawn in part a) the individual falls in
6. An estimate of individual’s percentile.
7. Why this signifies a health concern.
8. A suggested course of action.

Interpreting z-scores: Complete the following statements using your knowledge about z-scores.

a. If the data is weight, the z-score for someone who is overweight would be

• zero
• negative
• positive

b. If the data is IQ test scores, an individual with a negative z-score would have a

• average IQ
• high IQ
• low IQ

c. If the data is time spent watching TV, an individual with a z-score of zero would

• watch very little TV
• watch the average amount of TV
• watch a lot of TV

d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be

• negative
• positive
• zero

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 8.8 years, and standard deviation of 2.6 years.

Experience 7

If you randomly purchase one item, what is the probability it will last longer than 3 years?

Round answer to three decimal places

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.1 inches, and standard deviation of 5.8 inches.

What is the probability that the height of a randomly chosen child is between 49.6 and 63.9 inches? Do not round until you get your final answer, and then round to 3 decimal places.

Answer= (Round your answer to 3 decimal places.)

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.883 g and a standard deviation of 0.286 g. Find the probability of randomly selecting a cigarette with 0.282 g of nicotine or less.
P(X < 0.282 g) =
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P₇₀, the 70-percentile. This is the temperature reading separating the bottom 70% from the top 30%.

P₇₀ = °C

(Round answer to three decimal places)

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 5.7-in and a standard deviation of 0.8-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 2.3% or largest 2.3%.

What is the minimum head breadth that will fit the clientele?
min =

What is the maximum head breadth that will fit the clientele?
min =

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Suppose that you are an elementary school teacher and you are evaluating the reading levels of your students. You find an individual that reads 59.3 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 23 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 3.6 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.