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# Normal Distribution

### 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

### IQ Curve

IQ's have a mean of 100 and a standard deviation of 15. Find the IQ score that defines the top 2.5% of all IQ scores.

### 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

### Explain what it means to say that this variable is "normally distributed."

Give a brief description of the variable and whether the scale of measurement is nominal, ordinal, interval, or ratio, and why. Explain what it means to say that this variable is "normally distributed." Then, define probability value and explain how a probability value of .05 in this example is related to the normal curve.

### Independent Random Samples

Let X and Y be the respective means of two independent random samples, each of size 4, from the two respective normal distributions N( 10, 9) and N(3, 4). Compute Pr (X > 2 Y).

### If x is normally distributed with mean 12 and standard deviation 2, then P(x< or equal to 9) is...

P(z< or equal to 9/10) P(z< or equal to 3/2) P(z< or equal to 2/3) P(z< or equal to 3/4)

### 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

### Normal Distribution: For each letter grade, find the minimum score. What do you think of this grading scheme?

Grades on a midterm exam in a large biochemistry class are normally distributed with a mean of 75 and standard deviation of 9. The instructor wants to assign an A grade to the top 10% of scores, a B grade to the next 10%, and so on, with an F grade to all scores below the 60th percentile. For each letter grade, find the minimu

### 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

### Probability of normal distribution

21. A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for Mensa? 23. The time to complete a final examinat

### Probability Distributions of normal distribution

3. Delta airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. A. Show the graph of the probability density function for flight time B. What is the probability that the flight

### Z intervals raw scores

Let x be a random variable that represents the length of time it takes a student to write a term paper for Dr. Adam's Sociology class. After interviewing many students, it was found that x has an approximately normal distribution with mean &#956; = 6.8 hours and standard deviation &#963; = 2.1 hours. Convert each of the foll

### Probability and Sample Mean

The lifetime of a certain brand of batteries are known to be normally distributed with a mean of 1600 hours and a standard deviation of 400 hours. A random sample of 64 of these batteries is taken. What is the probability that the sample mean lifetime is more than 1500 hours?

### Statistics Problems

1. Find the area under the normal curve which is shaded on the graph. Use 4 decimal places. 2. For a standard normal distribution, find the percentage of data that are more than 1 standard deviation away from the mean. Use two decimal places. For example, 12.34% should be written as 12.34 3. The Precision Scientific Instru

### Distribution of x on a Symmetrical Shape

Let x be a random variable. The x distribution has a mean of 16 days. SD= 2 days The distribution of x values is more or less mound shaped and symmetrical but not necessarily normal. N=30 number of eggs in an incubator. Let x(with a line over it) be the average incubation times of eggs. a. what can we say about the probabil

### Statistics : Sampling Distributions and Sample Means

A random sample of size 25 is taken from a normal population having a mean of 80 and a standard deviation of 5. A second random sample of size 36 is taken from a different normal population having a mean of 75 and a standard deviation of 3. Find the probability that the sample mean computed from the 25 measurements will exceed

### Inverse Normal Distribution

SAT scores have a mean 500 and a standard deviation of 100 ACT scores have a mean of 18 and a standard deviation of 6. a. If a school accepts the top 10% what is the minimum ACT score and the minimum SAT score. b. If a school accepts the top 20% what is the minimum ACT and SAT score. c.If a school accepts the top 60% wh

### Calculation of probability based on normal distribution

Please show all work such as formula commands. The amount of money that a family of four will spend at Kings Island, including the food and souvenirs, is \$130 with a standard deviation of \$12. Assume that this distribution is normal. 1. Find the probability that a particular family of four selected at random spends between

### Normal Distribution Probability, z-scores, finding probabilities, proportions

Finding probability using Normal Distribution Question : Ina normal distribution, find the probability that a term picked at random has a z score: (a) Above z=1.85 (b) Below z= -1.23 (c) Between z= 1.5 and z= .5

### Define, Describe and Provide an Example of the Komologrov-Smirnov Distribution

Define, describe and provide an example of the Komologrov-Smirnov distribution. Show all your work in obtaining the answer.

### Normal Distribution Questions

1. A normal distribution has a mean of 50 and a standard deviation of 4. Determine the value below which 95 percent of the observations will occur. 2. A normal distribution has a mean of 60 and a standard deviation of 12. You select a random sample of 9. Compute the probability the sample mean is: A. Greater than 63

### What statistical tool should be used for the following? Random sampling. What if population isn't normal?

Please discuss the following: As regional manager for a retail store, you want to determine if consumers' income levels are related to their spending pattern. 1. What statistical tool should you use? 2. If you have to select a sample of your store's customers based on gender, how can you determine if the samplin