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Normal Distribution

Empirical Rule: Normal Distribution

The mean of land and buildings per acre from a sample of farms was $637, with a standard deviation of 26. Use Empirical Rule to find approximate percentage of acreage whose values were between $ 661 and $663. Approximate %

Random Walk Theory and Normal Distribution

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 properti

Assumptions of various tests

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

Radio station hypothesis tests

WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in: a. More than 20 minutes?

Normal distribution

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

Binomial distribution of home runs

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

Operations Research and Economic Order Quantity

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

Normal Distribution and Marketing

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.

Difference between uniform and normal probability distribution

What is an important difference between the uniform and normal probability distributions? The mean, median and mode are all equal . The mean and median are equal They are negatively skewed About 68% of all observations are within one standard deviation of the mean.

Statistics - Error and Confidence

The National Quality Research Center at the University of Michigan provides a quarterly measure of consumer opinions about products and services (The Wall Street Journal, February 18, 2003). A survey of 10 restaurants in the Fast Food/ Pizza group showed a sample mean customer satisfaction index of 71. Past data indicate that th

Determine the probability the sample mean

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

Random numbers

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?

Expectation of normal distribution

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

Shape of the Sampling Distribution

(See attached file for full problem description) A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: _ x = $50.00 a

Probability: Sample Proportions and Surveys

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

Random Selection and Normal Distribution

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


A company that sells annuties must base the annual payment on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. What pr

Descriptive Statistics and Faulty Computers

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

Determining Probability and Expected Profit: Doering Auto Sales

Ward Doering Auto Sales is considering offering a special service contract that will cover the total cost of any service work required on leased vehicles. From experience, the company manager estimates that yearly service costs are approximately normally distributed, with a mean of $150 and a standard deviation of $25. a. If

Normal Distribution and Sigma Calculations

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.

Primary Financial Statements

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

Questions on CREDIT SCORES

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

Distribution of grades

When dealing with college education one could argue that overall grades received by students follow a normal distribution or bell curve. Hence, grading on a curve (the standard bell curve or normal distribution) might be fair and mirror the overall trend of the student population. Do you think that this approach is fair? D

Standard normal random variables

Let Z be a standard normal random variable. Calculate the following probabilities and round your responses to at least three decimal places. P (Z > - 0.64) = P (Z &#8804;(less than or equal to) - 1.39) = P (1.38 < Z < 2.07) =

Normal Probability: Percent of Observations

The mean of normal probability distribution is 60; the standard deviation is 5. a. About what percent of the observations lie between 55 and 65? b. About what percent of the observations lie between 50 and 70? c. About what percent of the observations lie between 45 and 75? See the attached file.

Various Probability Problems

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

Critical Value and Probabilities

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

Mean, Normal Distribution, Standard Deviation

The mean starting salary for college graduates in the spring of 2004 was $36,280. Assume that the distribution of starting salaries follows the normal distribution with a standard deviation of $3,300. What percent of the graduates have starting salaries: a. Between $35,000 and $40,000? b. More than $45,000? c. Between $40,0

Simulation using Crystal Ball / OptQuest

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