A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 90 and standard deviation σ = 25. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)

(a) x is more than 60


(b) x is less than 110


(c) x is between 60 and 110


(d) x is greater than 125 (borderline diabetes starts at 125)

Solving these useing R program using pnorm() for Statistics

Please show the code you used and the answer Thank you

The fracture toughness (in ???√?) of a particular steel alloy is known to be normally distributed with a mean of 28.3 and a standard deviation of 0.77. We select one sample of alloy at random and measure its fracture toughness.

▶ What is the probability that the fracture toughness will be between 27.8 and 30.7?

▶ What is the probability that the fracture toughness will be at least 29.5?

▶ Given that the fracture toughness is at least 29, what is the probability that the fracture toughness will be no more than 30.5?

A random sample of n=100 observations produced a mean of x⎯⎯=30 with a standard deviation of s=5.

(a) Find a 99% confidence interval for μ
Lower-bound:  Upper-bound:

(b) Find a 95% confidence interval for μ
Lower-bound:  Upper-bound:

(c) Find a 90% confidence interval for μ
Lower-bound:  Upper-bound:

Suppose you are trying to determine the capacity (in gallons) of the gas tank needed on an airplane you are constructing. You want to be able to travel 3200 nautical miles without stopping, and have gathered data on the amount of fuel similar planes used during flights of comparable length. Show complete calculation and your steps, also interpetation and explanation as asked.

Consider a sample with the following properties: x̅ = 261.5, s = 18.73, n = 26

A) Calculate a confidence interval with α = 0.10

B) Calculate a confidence interval with α = 0.01

C) How would you interpret the results for the confidence interval from part B?

One of the costs of unexpected inflation is an arbitrary redistribution of purchasing power. Find the loser and winner of the following transactions. In other words, describe how the purchasing power is redistributed with these transactions. b. Jennifer took out a fixed-interest-rate loan from Bank H when the CPI was 100. She expected the CPI to increase to 103 but it actually increased to 105. c. Nick bought some shares of stock and, over the next year, the price per share decreased by 7 percent and the price level decreased by 9 percent. c. Nick bought some shares of stock and, over the next year, the price per share decreased by 7 percent and the price level decreased by 9 percent. d. Jackie saves $100 and receives $106 the next year. During the same year, the price of the basket of goods that she purchases increases from $100 to $104.e. Fifteen years ago T’s parents purchased some land with the idea of selling it later to help pay your college expenses. They purchased the land for $100,000. They sold if for $180,000. During the time they held it the price level rose from 80 to 120.f. One year ago Sam purchased bonds for $100,000. He just sold them for $120,000. During the year the price level rose by 5%.g. Mitch makes payments on a car loan. If the price level a year ago was 120 and people expected it to rise to 125 but it actually rose to 128.

The Decadent Desserts cookbook has recipes for desserts. The number of calories per serving for the recipes in the cookbook is normally distributed with a mean of 378 and a standard deviation of 34.5. If 18 recipes are randomly selected to serve at a reception, what is the probability that the average calories per serving for the sample is over 385?

Assume that females have pulse rates that are normally distributed with a mean of mu equals 73.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts​ (a) through​ (c) below. a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 79 beats per minute. The probability is ____. ​(Round to four decimal places as​ needed.) b. If 4 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 79 beats per minute. The probability is _____. ​(Round to four decimal places as​ needed.) c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30? A. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size. B. Since the distribution is of​ individuals, not sample​ means, the distribution is a normal distribution for any sample size. C. Since the mean pulse rate exceeds​ 30, the distribution of sample means is a normal distribution for any sample size. D. Since the distribution is of sample​ means, not​ individuals, the distribution is a normal distribution for any sample size.

A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20¢; 75¢; 50¢; 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal. You wish to conduct a hypothesis test (α = 0.05 level) to determine if the mean cents off for coupons is less than 50¢.

1. State the null and alternate hypotheses clearly.
2. Conduct the hypothesis test based on the test statistic and critical value(s). Clearly indicate each.
3. What is the p-value? Use the p-value to conduct the same test
4. Report your conclusion in words, in the context of the problem.
5. What is the power of the for an alternative hypothesis value of 49¢?

If x is a binomial random variable, compute P(x) for each of the following cases:

(a)  P(x≤5),n=9,p=0.7P(x≤5),n=9,p=0.7

(b)  P(x>1),n=9,p=0.1P(x>1),n=9,p=0.1

(c)  P(x<3),n=5,p=0.6P(x<3),n=5,p=0.6

(d)  P(x≥1),n=6,p=0.9P(x≥1),n=6,p=0.9

Using the info below, answer the next following questions:

A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20¢; 75¢; 50¢; 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal.

(a) Determine the sample mean in cents (Round to 3 decimal places)

(b) Determine the standard deviation from the sample . (Round to 3 decimal places)

(e) Construct a 95% confidence interval for the population mean worth of coupons.  Use a critical value of 2.16 from the t distribution.

What is the lower bound? ( Round to 3 decimal places )

(f)  Construct a 95% confidence interval for the population mean worth of coupons .

What is the upper bound? ( Round to 3 decimal places )

4. (a) In a fraud detection system a number of different algorithms are working indepen- dently to flag a fraudulent event. Each algorithm has probability 0.9 of correctly detecting such an event. The program director wants to be make sure the system can detect a fraud with high probability. You are tasked with finding out how many different algorithms need to be set up to detect a fraudulent event. Solve the following 3 problems and report to the director. [Total: 18 pts] (b) Suppose n is the number of algorithms set up. Derive an expression for the probability that a fraudulent event is detected. (6 pts) (c) Using R, draw a plot of the probability of a fraudulent event being detected versus n, varying n from 1 to 10. (6 pts) (d) Your colleague claims that if the company uses n = 4 algorithms, the probability of detecting the fraudulent event is 0.9999. The director is not convinced. Generate 1 million samples from Binomial distribution with n = 4, p = 0.90 and count the number of cases where Y = 0. Report the number to the director. (6 pts)

Thoroughly answer the following questions:

What is the difference between prevalence and incidence? Provide an example of each. Do not provide the definitions, explain in your own words.

The weights of 22 randomly selected mattresses were found to have a standard deviation of 3.17. Construct the 95% confidence interval for the population standard deviation of the weights of all mattresses in this factory. Round your answers to two decimal places.

1. A social psychologist wanted to determine whether attitudes of men toward abortion were different in rural and urban areas. He prepared a questionnaire and administered it to a group of city dwellers and a group of country dwellers. Each city man was matched with a country man on age, income, and education. High scores indicate positive attitudes towards abortion. The data:

1. What can the social psychologist say about differences in the attitudes of rural and urban men?
2. Justify the statistical method you used to analyze the data.