### Two Normal Distribution Papers

(See attached files for full problem description)

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(See attached files for full problem description)

A) For the two hypothetical leagues represented below calculate the league standard deviation (s t) of the winning percentage (wti) for each year. {Where wti is the winning percentage of team i in year t; st is the standard deviation of the winning percentages in one of the leagues in year t; and w is calculated as the number of

Problem 1 A recent report in USA Today indicated a typical family of four spends $490 per month on food. Assume the distribution of food expenditures for a family of four follows the normal distribution, with a mean of $490 and a standard deviation of $90. a. What percent of the families spend more than $30 but less than $490

Please see the attached file "Q11.5.doc" for the problem statement. suppose that w is normal and has expected value a and variance sigma^2. so the expected value of u = exp(w) is exp(a + 0.5sigma^2). What is the variance of u: var(u)?

Please help me with an assignment by answering the following: A manufacturer claims that the life span of its products is normally distributed, with a mean of 21.9 hours and a standard deviation 102 hours. A test is made of 20 products and the sample time are shown below. Find the mean and the standard deviation of the sample

Ms. Lisa Monnin is the budget director for nexus media inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information: Sales ($): 131,135,146,165,136,142 Audit ($): 130,102,129,143,149,120,139 At the .10 significance level, can she conclude

Attached is the daily closing price of the stock (xmsr). Decide whether the data appears to be normally distributed by: 1. record the daily changes in the closing stock price of each day. a. make a stem and leaf display, histogram or polygon, and box and whisker plot. b. evaluate the actual versus theoretical proper

A work-study engineer times a certain operation, and discovers that the average time it takes is 10 minutes, but on 15% of occasions it takes more than 13 minutes. Assuming that times for the operation follow a normal distribution, what is its standard deviation?

1. What are the only three ways to setup the Hypothesis (Ho & H^)? ( the last symbol "^" is in the bottom of the H) 2. What are the assumptions regarding a large one sample z-test and what Excel aid would you use to perform the test, Data Analysis or MacDolt? 3. What are the assumptions regarding a small one sample t-test

If 65% of the population of a large community is in favor of a proposed rise in school taxes, approximate the probability that a random sample of 100 people will contain a) at least 50 who are in favor of the proposition b) between 60 and 70 inclusive who are in favor c) fewer than 75 in favor

In 1998, Mark McGwire of the St. Louis cardinals hit 70 home runs, a new Major League record. Was this feat as surprising as most of us thought/ In the three seasons before 1998, McGwire hit a home run in 11.6% of his times at bat. He went to bat 509 times in 1998. If he continues his past performance, McQwire's home run count i

A product sold by Home Depot, Inc., with an annual demand of 1000 units has Co = $25.50 and Ch = $8. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with µ = 25 and standard deviation = 5. a. Determine the recommended order quantity. b. Determine the reorder p

The proportion of defective telephones manufactured on Mondays is 0.3. If a sample of 20 telephones is selected, what is the probability that 5 of the phones in the sample are defective? Use the normal distribution to approximate the binomial. Since this is a continuous distribution approximating a discrete distribution, use

When is understanding the normal distribution and the factors that affect its shape important in solving business and marketing-related questions? Explain with a simple example.

The mean television viewing time for Americans is 15 hours per week (Money, November 2003). Suppose a sample of 60 Americans is taken to further investigate viewing habits. Assume the population standard deviation for weekly viewing time is 4 hours. a. Determine the probability the sample mean will be within 1 hour of the pop

A normal distribution has a mean of 500 and a standard deviation of 50. A manager wants to simulate 2 values from this distribution, and has drawn these random numbers: -0.6 and 1.4. What are the 2 values respectively?

I know this problem is very easy, finding E(x) from the distribution function. I tried to do it by integration by parts, one way I took x to be my first function and the whole exp term to be my 2nd function, but it didn't work, then I split the exponential term to 2 terms combined one with x as my first function and took the sec

Approximately 5% of U.S. families have a net worth in excess of $1 million and thus can be called millionaires. However, a survey in the year 2000 found that 30% of Microsoft's 31,000 employees were millionaires. If random samples of 100 Microsoft employees had taken that year, what's the probability that the sample proportion

The diameter of a Ping-Pong ball manufactured at a factory is expected to be approximately normally distributed with a mean of 1.30 inches and a standard deviation of 0.04 inch. What is the probability that a randomly selected Ping-Pong ball will have a diameter between 1.31 and 1.33 inches? A. 0.0987 B. 0.1747 C. 0.2734

(See attached file for full problem description) --- 4. Consider independent random variables, Xi, where Let Y = (a) Determine fY (y). Describe this distribution. Hint: This is probably easiest using moment generating functions.

A computer laboratory in a school has 33 computers. Each of the 33 computers has a 90% reliability. Allowing for 10% of the computers to be down, an instructor specifies an enrollment ceiling of 30 for his class. Assume that a class of 30 students is taken into the lab. a. What is the probability that each of the 30 students

Assume that the life in hours of a radio tube is normally distributed with mean 100 hours. If a purchaser requires at least 90 percent of them to have lives exceeding 80 hours, please show that the largest value that sigma can have and still have the purchaser satisfied is 15.6.

1. Can you please provide a description of the 3 primary financial statements (balance sheet, income statement, and statement of cash flows) and what each statement tells users about an organization 2. Explain the components of each statement (assets, liabilities, equity, revenues, expenses) 3. Explain the set of activiti

Whenever you apply for credit someone will check your credit score. Here is some data obtained from one of the agencies that administers the credit score. The following is a distribution of FICO scores across the country: a. Over 800-11% of the population b. 700-800 - 49% of the population c. 600-700 - 27% of the pop

11. An automaker guarantees its particular type of automotive transmissions for 90,000 km. Tests have shown that such transmissions have an average life of 135,000 km with a standard deviation of 22,500 km. If the lives of these transmissions are normally distributed, what is the probability that a car will be returned to the

Please find attached problem. (a) A five-gear assembly is put together with spacers between the gears. The mean thickness of the gears is 5.030 cm with a standard deviation of 0.008cm. The mean thickness of the spacers is 0.140 cm with the standard deviation of 0.005 cm. Find the mean and standard deviation of the assembled u

How do you develop a bell curve for 1,000 cases: With a given mean of 20 and a standard deviation of 2, how do you compute the -3,-2,-1 (mean), +1,+2,+3 points along the baseline of the curve (assuming the curve is normal)? Then repeat the mean of 10 pounds and the standard deviation is 4.5. Repeat again with a mean of 4 secon

4. (1) Assume that the readings on the thermometers are normally distributed with a mean of 0o and standard deviation of 1.00o C. A thermometer is randomly selected and tested. Draw a diagram and find the probability in degrees. Between -1.18 and 2.15 (2) The lengths of pregnancies are normally distributed with a mean of 2

This problem requires the use "Crystal Ball", the popular commercial spreadsheet add-in. For clarity, it is distributed by Decisioneering, Inc. This problem specifically requires that Excel and "Crystal Ball" (and OptQuest as applicable) be used - and not any other software choices. The link below directs you to a free 7-day t

Let x1 and x2 be independent normal random variables, x1 n(ui,oi2), and let y1 = x1 and y2 = x1+x2