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Normal Distribution

Normal Probability : key information

Let's assume you have taken 100 samples of size 36 each from a normally distributed population. Calculate the standard deviation of the sample means if the population's variance is 25. Find P(9 < x < 15) when mu = 12 and sigma = 2. Write your steps in probability notation. Find P(x = 13) for a sample taken from a normally

Standard Deviation

Suppose that scores on a particular test are normally distributed with a mean of 120 and a standard deviation of 19. What is the minimum score needed to be in the top 5% of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.

Options Pricing

See attached file for full problem description. summary of options purchased at beginning of 4th quarter with 3 months to expiration (european style options) position shares premium strike price long calls 63,000 $20.45 $110 long puts 63,000 $13.15 $110 beginning end 4th Quarter 4th Quarter underly

An executive at Westinghouse drives from his home in the suburbs near Pittsburgh to his office in the center of the city. The driving times are normally distributed with a mean of 35 minutes and a standard deviation of 8 minutes.

An executive at Westinghouse drives from his home in the suburbs near Pittsburgh to his office in the center of the city. The driving times are normally distributed with a mean of 35 minutes and a standard deviation of 8 minutes. a. In what percent of the days will it take him less than 30 minutes to drive to work? b.

Mean of a normal distribution is 400 pounds

What is the area between 415 pounds and the mean of 400 pounds? What is the area between the mean and 395 pounds? What is the probability of selecting a value at random and discovering it has a value of less than 395 pounds?

Project Management, Queuing, and Simulation

1. The use of simulation to examine corporate operations (industrial dynamics), national economies (econometric models), and urban governments is known as A. Monte Carlo Methods B. Operational Gaming C. System Simulation D. Queuing Methods 2. PERT A. Is a network technique that uses three time estimat

Statistics Concepts: Cases and Observations

14. Approximately ______ of the area (cases or observations) under the normal curve is found between 1 standard deviation above and 1 standard deviation below the mean. 15. What percentage of area (or cases or observations) is found above a z value of 1.96? ._____ 16. A random sample of 20 observations is drawn from a

Normal random variable and probability

The number of passengers on the Carnival Sensation during one-week cruises in the Caribbean follows the normal distribution. The mean number of passengers per cruise is 1,820 and the standard deviation is 120. 1. What percent of the cruises will have between 1,820 and 1,970 passengers? 2. What percent of the cruises will ha

Sampling and Standard Error

13. The quality assurance department for Pepsi Distributors, Inc. maintains meticulous records on the bottling line for two-liter Pepsi bottles. Records indicate that the process follows the normal probability distribution with a mean amount per bottle of 2.01 liters and a standard deviation of 0.025 liters. The foreman random

Statistics on Skin Cancer Malignancies

#2 There is some concern that exposure to gases used in anesthesiology may be harming the health of anesthesiologists. In one study of 525 Michigan nurse anesthesiologists, 10 reported a new malignancy other than skin cancer during the previous year. 2.1 What is the appropriate choice of distribution for the incidence of ne

Statistics - Normal Distribution and Probability

See the attached file. 16. For a normal population with mean=50 and standard deviation=10, what is the probability of obtaining a sample mean greater than 52 for each of the following sample sizes n=5 _________________% n=10 _________________% n=50 _________________% n=100 _________________% An assessment of optimism

Probability of normal distribution problem

1. Find the area under the Normal Distribution from the mean to a z-score of -2.07. 2. Find the z-score that corresponds to an area of 0.5557 under the Normal Distribution. 3. The average age of statistics students nationwide is 22. The standard deviation is 2.5 years. Assume the age is a normally distributed variable

Standard normal distribution used to compute probabilities

1. Given that z is a standard normal random variable, compute the following probabilities. a. P(-1≤z≤0) b. P(-1.5≤z≤0) c. P(-2<z<0) d. P(-2.5≤z≤0) e. P(-3≤z≤0) 2. Given that z is a standard normal random variable, compute the following probabilities. a. P(0≤z≤.83) b. P(-1.57≤z≤0) c. P(z>44) d

Mean and standard deviation

The following table displays information on the abortion rate- the number of abortions per 1,000 women- for each U.S. state and the District of Columbia in 2000. a. What are the mean and the standard deviation for the abortion rate for all states? b. Using the information from (a), how many states fall more than 1 standard dev

Empirical Rule and Chebychev Inequality

If Chebychev Inequality gives the lower bound for probability. For the present problem the lower bound for the probability is 0.75 and actual probability is 0.87. There is no contradiction between empirical rule and Chebychev Inequality Given percentage (87%), does the empirical rule apply? What does the Empirical Rule s

Chebyshev's theorem and normal distribution

Given a normal distribution of data, we know from the Empirical Rule that in between 2 standard deviations from the mean (i.e. xbar - 2s..to..xbar + 2s) there lies about 95% of all the data. Calculate and show the percentage of data from xbar - 2s..to..xbar + 2s using Chebyshev's theorem. Now, if I told you that a cer

Equations Rewritten

Give a brief description of the variable and whether the scale of measurement is nominal, ordinal, interval, or ratio, and why. The Measurement Principles Nominal : People or objects with the same scale value are the same on some attribute. The values of the scale have no 'numeric' meaning in the way that you usually think

Sample Mean

The mean annual salary for employees at Company X is $78,000. If we assume a standard deviation of $12,000, what is the sampling distribution of the sample mean for samples of size 121?

Normal Distribution/Standard Deviation - Shoe Sizes

Suppose the shoe size of workers is normally distributed, with a mean of 10.0 inches, and a standard deviation of 0.5 inch. A clueless shoe manufacturer is going to introduce a new line of shoes specifically for these workers. Assume that if the shoe size falls between two shoe sizes, you purchase the next larger shoe size. H

Statistics : Neyman Factorization Theorem

Please provide steps so that I can understand the process of finding sufficient statistics using the Factorization Theorem. Let X1, X2,...,Xn be a random sample from the normal distribution N(0,THETA), 0 < THETA < +infinity. Show that "(the sum from 1 to n of (Xi^2))" is a sufficient statistic of THETA. What is inside eq

Normal Distribution Investigation

A machine that fills quart orange juice bottles is set to fill them with 32.1 oz. If the actual contents of the cartons vary normally, with a standard deviation of .1 oz, what percent of the cartons contain less than a quart (32 oz).

Normal Distribution: sample mean, standard error of mean, probability

1. A population of unknown shape has a mean of 75. you select a sample of 40. the standard deviation of the sample is 5. What is the probability that the sample mean is between 76 and 77? a. 0.3980 b. 0.8905 c. 0.0081 d. 0.3943 2. a population has a mean of 50 and a standard deviation of 12. FOr samples of size 9, sam

Calculation of probability based on normal distribution problem

1. The length of time a customer must wait in line at the post office has approximately a normal distribution with a mean of 5.8 minutes and a standard deviation of 2.6 minutes. Find the probability that the customer will wait between 4 and 8 minutes. 2. The lifetime of a certain brand of tire follows an approximately normal

Excel Spreadsheet that Plots a Bell Curve

I would like to have an Excel file (that is: MyChart.xls) that will chart a Gaussian curve for me (a 'normal bell curve'). I would like the various parameters that affect the shape of the curve "separated out" (that is, put in separte cells) so I can independently change them...so I can easily see the effect on the chart. [T

Calculations based on Normal distribution such as probability in an interval

1 The distribution of purchase amounts of customers of a popular retail store is normal with a mean of $25 and a standard deviation of $8. a. What percentage of customers spends less than $35? b. What percentage of customers spends between $15 and $35? c. Find the dollar amount such that 80% of customers spend at least t

Normal Distribution

Suppose that IQ scores in one region are normally distributed with a standard deviation of 16. Suppose also that exactly 55% of the individuals from this region have IQ scores of greater than 100 (and that 45% do not). What is the mean IQ score for this region? Carry your intermediate computations to at least four decimal plac