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Normal Distribution

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?

Verifying the Assumption of a Normal Distribution

How do you verify that the assumption of a normal distribution is correct if you have only the mean and standard deviation? What could you do if you actually have the data? In my case, the sample size is 1000; mean 40, and SD 10. If you then took a sample of 20 from the original sample of 1000, is the expected value 40? How

Probability and Samples

I have a random sample of n = 16 scores with a normal distribution, mean of 50 and standard deviation of 10. I need to calculate what range of values has a 95% probability of containing the sample mean. Here is where I get stuck. I have been provided the answer and it is 45.13 to 54.87 (50 +/- 4.87). I don't know how to

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

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 th

Standard distribution, deviation, etc.

15. If P(A) = 0.4, P(B| A) = 0.35, P(A  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Y) = a. 0.0944 b. 0.6150 c. 1.0000 d. 0.0000 27. For a standard normal distribution, the probability of z  0 is

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

Choosing C

Test Taking When taking a multiple choice test, the old adage comes to mind: 'When in doubt, Pick C'. It turns out that this is true in many cases. On a multiple choice test, with four solutions, the middle two choices tend to be the most correct answers. This presents a Gaussian (normal) distribution for the choices A,

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

Engineering Stats

Assume that (X,Y) is a two-dimensional continuous random variable with pdf... a) Compute the probability that X + Y ? 1. Please see attached for full question.

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

Stepwise 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

Binomial pdf

The number of days per year that it snows in an eastern Idaho town is normally distributed with a mean of 25 days and a standard deviation of 5.4 days. 1. What is the chance that it snows exactly 25 days?

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


6.38 Obtain the z-score that has an area of .95 to its right. 6.40 Find the following z-scores a. z0.03 b. z0.005

Normal distribution

6.12 a. The area under the standard normal curve with parameters m = 64.4 and o= 2.4 that lies to the left of 61 is 0.0783. Use this information to estimate the percentage of female's students who are shorter than 61 inches. 6.14 According to the National Health and Nutrition Examination Survey, the serum (noncellular portio

Using Excel to make plots of Gaussian distribution

I am using Analytical Chemistry 7th edition By Skoog, West, Holler, and Crouch. please let me know if any additional info. is needed. There is a sample of the graph in the book Chapter 6 and 7. Using Excel, construct a spreadsheet to make two plots of a Gaussian distribution: 1. relative frequency vs deviation from the mean

Basic Statistics Problem (Normal Distribution; Mean; Standard Deviation)

I am having trouble with PART B of this problem. Here is the whole problem: Assume body temperatures are normally distributed with mean of 98.2 and a standard dev. of 0.62 Part A) Assuming a hospital defines a fever as 100 or over, determine the percentage of a normal healthy person considered to have a fever using Z tabl