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# Normal Distribution

### 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

### 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

### 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

### Probability and Statistics : Scatter Plot, Line of Best Fit, Extrapolation and Forecasting

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

### 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

### 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

### Random variable

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

### ESP and Statistics

I need some help answering this question without calculus: In 1973, Charles Tart ran an experiment at UC Davis to test for ESP abilities. Tart used an electronic random number generators called the Aquarius with four "targets". The machine randomly picked one of the fours targets, and the subject guessed which target the machi

### Moment of Inertia: Parallel axis theorem

(See attached file for full problem description with equations) (Steiner's theorem) If IA is the moment of inertia of a mass distribution of total mass M with respect to an axis A through the center of gravity, show that its moment of inertia IB with respect to an axis B, which is parallel to A and has the distance k from it,

### Normal distribution

The resistances of carbon resistors of 1500 ohm nominal value are normally distributed with µ = 1500 and standard deviation = 200. a. What proportion of resistors is expected to have resistance greater than 1150 ohm? b. Within plus and minus what amount around the mean do 80 percent of resistances fall?

### Trail Making Test and Noise pollution questions.

(See attached file for full problem description) --- 1. The Trail Making Test (TMT) is frequently used in neuropsychological assessment to provide a quick estimate of brain damage in humans. To investigate the neuropsychological deficits in alcoholics, 50 problem drinkers (25 drinkers under the age of 40 and 25 drinkers 40 y

### Normal Distribution: Mean Labor Cost to Repair a Heat Pump

A recent article in the Cincinnati Enquirer reported that the mean labor cost to repair a heat pump is \$90 with a standard deviation of \$22. Monte's Plumbing and Heating Service completed repairs on two heat pumps this morning. The labor cost for the first was \$75 and it was \$100 for the second. Compute z values for each and com

### Lee County Georgia Weekly Wages Sampling Distribution

In Lee County Georgia the distribution of weekly wages for workers in the construction industry is skewed to the right with mean equal to \$473 (Georgia Department of Labor, Labor Market Information, 1999). Assume the standard deviation of the distribution is \$25. An economist plans to randomly sample 40 workers in Lee County and

### Normal Distribution - Linear Model Problem

(See attached file for full problem description) Let , i=1, 2, ...,m be a simple regression, where xi unobservable and assumed to be independent and identically distributed with common distribution Instead, we assume that, for each xi, zi1, zi2, . . . , zin are observed. Given xi, the conditional distribution for the obs

### Single Period Inventory Model with Probabilistic Demand : Recommended Order Quantity

The Fitness Shop is considering ordering a special model exercise machine. Each unit will cost the shop \$220 and it will sell for \$400. Any units not sold at the regular price will be sold at the year-end model clearance for \$150. Assume that demand follows a normal probability distribution with µ = 10 and variance = 3. What is

### Standard distribution, deviation, etc.

15. If P(A) = 0.4, P(B| A) = 0.35, P(A &#61640; B) =0.69, then P(B) = a. 0.14 b. 0.43 c. 0.75 d. 0.59 18. If X and Y are mutually exclusive events with P(X) = 0.295, P(Y) = 0.32, then P(X&#61629;Y) = a. 0.0944 b. 0.6150 c. 1.0000 d. 0.0000 27. For a standard normal distribution, the probability of z &#61603; 0 is

### Find the specific data value (percentile) from a normal distribution.

Please see attached file. Please show all work. If the mean weight of women in the U.S. is 143.0 and the standard deviation is 29.0, what is the weight that separates the bottom 24% from the top 76% of women?

### Normal distribution and Standard Error of the Mean

5. A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. a. The professor has informed us that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A? b. Students who made 57.93 or

### Sampling Distribution, Mean and Standard Deviation

See attachment for better symbol representation. 1) A manufacturer of paper used for packaging requires a minimum strength of 20 pounds per square inch. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour's production and a strength measurement is recorded

### 7 Elementary Statistics Problems - dice probability and normal distribution

Problems must be worked out so that the average first year college student can understand them. 1. If a gambler rolls two dice and gets a sum of 10. he wins \$10, and if he gets a sum of three, he wins\$20. The cost to play is \$5. What is the expectation of this game? 2. A recent study found that the average life expectan

### Normal probability distribution..

Birth weights of babies born to full-term pregnancies follow roughly a normal distribution. At Meadowbrook Hospital, the mean weight of babies born to full-term pregnancies is 7 lbs with a standard deviation of 14 ounces (1 pound = 16 ounces). a. Dr. Watts has 4 deliveries (all for full-term pregnancies) coming up during the

### Problems on sampling, hypothesis testing and confidence interval

1.Which of the following statements about the sampling distribution of the sample mean is incorrect? a. The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n>30). b. The sampling distribution of the sample mean is generated by repeatedly taking samples of size n

### Probability: Standard Deviation, Exponential Distribution and Expected Values

(8) 1. A manufacturer of electronics products expects that 1% of units fail during the warranty period. A sample of 600 independent units is tracked for warranty performance. a) What is the expected number of failures during the warranty period? b) What is the probability that none fails during the warranty period? c) What is

### Case Study using normal distribution

A company supplies pins in bulk to a customer. The company uses an automatic lathe to produce the pins. Due to many causes - vibration, temperature, wear and tear, and the like - the lengths of the pins made by the machine are normally distributed with a mean of 1.012 inches and a standard deviation of 0.018 inch. The custome

### Significance Testing Format

The most important material reclaimed from beverage bottles is PET plastic. A serious impurity is aluminum, which later can clog the filters in extruders when the recycled material is used. The following are the amounts (in ppm by weight of aluminum) found in bihourly samples of PET recovered at the plant over roughly a two day

### Find Percentiles from a Given Normal Distribution

Your firm is attempting to reduce its cost of maintenance of customers by culling the least-productive of them. A census of sales records was undertaken and it was determined that the mean level of sale of all customers was \$235,000 with a standard deviation of \$15,000. (a) It is your desire to eliminate from your customer po