CASE STUDY: Chest Sizes of Scottish Militiamen (p. 306):

1. The population mean and population standard deviation of the chest circumferences are 39.85 and 2.07, respectively, identify the normal curve that should be used for the chest circumferences
2. Use the table above to find the percentage of militiamen in the survey with chest circumference between 36 and 41 inches, inclusive. Note: as the circumferences were rounded to the nearest inch, you are actually finding the percentage of militiamen in the survey with chest circumference between 35.5 and 41.5 inches
3. Use the normal curve you identified in part (a) to obtain an approximation to the percentage of militiamen in the survey with chest circumference between 35.5 and 41.5 inches. Compare your answer to the exact percentage found in part (b).

At one point the average price of regular unleaded gasoline was $3.53 per gallon. Assume that the standard deviation price per gallon is ​$0.07

per gallon and use​ Chebyshev's inequality to answer the following.

​(a) What percentage of gasoline stations had prices within 3 standard deviations of the​ mean?

​(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean? What are the gasoline prices that are within 2.5 standard deviations of the​ mean?

​(c) What is the minimum percentage of gasoline stations that had prices between $3.39 and $3.67​?

​(a) At least _​__% of gasoline stations had prices within 3 standard deviations of the mean.(Round to two decimal places as​ needed.)

​(b) At least ___% of gasoline stations had prices within 2.5 standard deviations of the mean.​(Round to two decimal places as​ needed.)

The gasoline prices that are within 2.5 standard deviations of the mean are ​$_to ​$_.​(Use ascending​ order.)

​(c) _​__% is the minimum percentage of gasoline stations that had prices between $ 3.39 and $3.67.

6. Unanticipated changes in the rate of inflation

Initially, Neha earns a salary of $400 per year and Lorenzo earns a salary of $200 per year. Neha lends Lorenzo $100 for one year at an annual interest rate of 20% with the expectation that the rate of inflation will be 16% during the one-year life of the loan. At the end of the year, Lorenzo makes good on the loan by paying Neha $120. Consider how the loan repayment affects Neha and Lorenzo under the following scenarios.

Scenario 1: Suppose all prices and salaries rise by 16% (as expected) over the course of the year. In the following table, find Neha's and Lorenzo's new salaries after the 16% increase, and then calculate the $120 payment as a percentage of their new salaries. (Hint: Remember that Neha's salary is her income from work and that it does not include the loan payment from Lorenzo.)

Scenario 2: Consider an unanticipated decrease in the rate of inflation. The rise in prices and salaries turns out to be 5% over the course of the year rather than 16%. In the following table, find Neha's and Lorenzo's new salaries after the 5% increase, and then calculate the $120 payment as a percentage of their new salaries.

An unanticipated decrease in the rate of inflation benefits   and harms   .

An apple orchard farmer wants to know the true population proportion of all apples harvested at their farm which have the less valuable condition of being blemished, or in other words, are cider apples.

This true population proportion is a parameter value represented by the symbol p. As a population parameter, this value can never be known with certainty. It can however, be estimated with varying levels of confidence.

To estimate this parameter p, the farmer draws a simple random sample (SRS) of 524 apples from the orchard. Within this sample, the farmer finds that exactly 47 of the apples are cider apples.

The farmer then computes a 96%-level confidence interval estimate for the parameter p.

In percentage form, and rounded to four digits past the decimal point: What is the approximate value of the Lower Limit of this confidence interval?

Include a percentage symbol at the end of your numerical answer (with no spaces).

In percentage form, and rounded to four digits past the decimal point: What is the approximate value of the Upper Limit of this confidence interval?

Include a percentage symbol at the end of your numerical answer (with no spaces).

In percentage form, and rounded to four digits past the decimal point: What is the approximate value of the Margin of Error for this confidence interval?

Include a percentage symbol at the end of your numerical answer (with no spaces).

Suppose the farmer now wishes that they had instead built a confidence interval with a 99% confidence level, and a margin of error no greater than 2%.

To achieve these new specifications: The farmer intends to draw another SRS of apples in the future, and build another confidence interval.

What minimum sample size of apples will the farmer have to draw, in order to achieve these new confidence interval specifications?

(Note: Your answer should be a whole number here.)

A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a​ two-candidate election, if a specific candidate receives at least 54% of the vote in the​ sample, that candidate will be forecast as the winner of the election. You select a random sample of 100 voters. Complete parts​ (a) through​ (c) below.

a.

The probability is ______ that a candidate will be forecast as the winner when the population percentage of her vote is 50.1​%.

b.

The probability is _____that a candidate will be forecast as the winner when the population percentage of her vote is 56​%

c.

- If this client was in a hospital setting for multiple days, what information could a nurse use to educate the client and what benefits would this provide for the Client? Question must be answered in paragraph form, no short answers can be accepted for the assignment.

"Case Study Mrs. S, a 45-year-old woman, came to your doctor’s office because she had a sore that would not heal on her leg. She is 5 ft 5 in. and weighs 200 lb (body mass index [BMI] = 33.5). Vital signs are temperature 98.6°F, pulse 70 beats per minute, respirations 16 breaths per minute, and blood pressure 160/95 mm Hg. Mrs. S reports a gradual increase in her weight since her third child was born 20 years ago. That baby weighed 12 lb. Two previous pregnancies produced infants weighing 10 and 11 lb. She has no known allergies. None of the children live at home. Mrs. S lives with her husband, who works as a construction laborer. She has been seasonally employed as a hotel maid at a nearby resort. Health insurance coverage is sporadic. They have a new insurance policy now. Mrs. S is the oldest of six children. Her father died of a heart attack at age 60. Her mother died of a stroke at age 62. Both parents reportedly “had a little sugar.” The sister who is closest to Mrs. S in age developed diabetes 3 years ago and is being treated with oral medication. Their youngest sister was diagnosed with type 1 diabetes at age 18 after an episode of mumps. Mrs. S reports a good appetite and a fluid intake of about 3 quarts per day. Her favorite beverage is iced tea with sugar and lemon. She does most of the grocery shopping and cooking. Mrs.S, hit her left ankle with the screen door about 2 months ago. The resulting sore has not healed but has gotten worse. Mrs. S knows that a sore that does not heal is a sign of cancer, which is why she sought medical attention. The ankle now has an open lesion 5 cm in diameter over the lateral ankle bone. The entire foot is swollen to twice the size of the right foot. The bandage over the sore had greenish-yellow drainage on it. A random blood glucose test 3 hours after her last meal shows a glucose level of 400 mg/dL. Her urine glucose was negative for ketones. The physician diagnoses Mrs. S with type 2 diabetes.