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# Normal Distribution

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### The average monthly gasoline purchase for a family with 2 cars is 90 gallons.

(TCO 6) The average monthly gasoline purchase for a family with 2 cars is 90 gallons. This statistic has a normal distribution with a standard deviation of 10 gallons. A family is chosen at random. (a) Find the probability that the family's monthly gaoline purchases will be between 88 and 98 gallons. (b) Find the probabilit

### Explain standard scores, normal distribution, measures of variability, function of norms

First, explain the purpose of transforming raw scores into standard scores. Describe what "normal distribution" means. Next, briefly describe measures of variability, and explain how they might help you understand assessment data. Finally, describe the function of norms in psychological assessment. Include the following in

### Statistics: Multiple Choice Questions

1. An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is know to be \$1,000. A random sample of 50 individuals resulted in an average income of \$15,000. What sample size would the economist need to use if he wants a 95% confidence interval no wider than plu

### T and Z calculations represented on a bell curve

T and Z tests are parametric tests that are designed to measure the differences in behavior between a sample population and a universal population. How is the T/Z calculation represented on a bell curve? Is it a standard deviation or variance?

### Statistics and Probability Sample Problems

1. In a recent study 90 percent of the homes in the United States were found to have color TVs. In a sample of nine homes, what is the probability that: a. All nine have color TVs? b. Less than five have color TVs? c. More than five have color TVs? d. At least seven homes have color TVs? 2. Thirty percent of the populatio

### Normal Distribution

A) What is normal distribution? b) given a certain data set, how can you determine whether the data set is normally distributed or not? c) Why do we want to test if the data is normally distributed?

### Normal distribution is so widely observed in daily life. Please provide an example.

Normal distribution is so widely observed in daily life. Please provide an example.

### Standard Normal Distribution: Fill in the blanks

Can you show work on the last set of problems I attempted to do the first two problems however, I don't know if that is right. Thanks 2. Assume the standard normal distribution. Fill in the blanks (a) P( z < 2.00 ) = .9773 (b) P( z < -1.24 ) = .1075 (c) P( z > ) = .0793 (d) P( z > ) =

### Statistics.

Confidence Interval Estimation 2. Compute a 95% confidence interval for the population mean, based on the sample 15, 17, 13, 14, 15, 14, and 59. Change the number from 59 to 14 and recalculate the confidence interval. Using the results, describe the effect of an outlier or extreme value on the confidence interval.

### Solving for Asymptotic Distribution

Please see the attached jpeg, thanks for your help: Let XI, , Xk be multinomial MN(n,Pi P2, • • . ,Pk) with EXi = 71)E n = 1. For k = 2 , nn,12 derive the asymptotic distribution of Q = E k oc= npir" . i=i

### Plot the vehicle stopping distance versus the speed of travel

Question 1 The distance Y necessary for stopping a vehicle is a function of the speed x of the vehicle. Suppose the following set of data were observed for 12 vehicles travelling at different speeds as shown in the table below. Vehicle No. Speed, kph Stopping Distance, m 1 40 15 2 9 2 3 100 40 4 50 15 5 15 4 6 65 25

### Finding Mean, Median, Mode, Sample Variance and Range

The heights of 10 sixth graders are listed in inches: {54, 62, 54, 57, 60, 61, 53, 63, 59, 56}. (a) Find the mean, median, mode, sample variance, and range. (b) Do you think that this sample might have come from a normal population? Why or why not?

### Statistics Sample Problems

1. Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is \$110,000. This distribution follows the normal distribution with a standard deviation of \$40,000. a. If we select a random sample of 50 households, what is the standard error of the mean?

### Research and Evaluation: Example Problem

What are some examples of literature reviews and statistics used and available at your work place or organization? What are they used for and how are they determined? What are the advantages and disadvantages of using surveys to conduct research? What is an example of a loaded question? In what situations is it appropriate t

### Distribution

Give an example representing a discrete probability distribution and a continuous probability distribution. Explain why your choice is discrete and continuous. Carefully define a standard normal distribution. Why does a researcher want to go from a normal distribution to a standard normal distribution? Explain.

### Normal distributions: distribution of sums

A straight rod is formed by connecting three sections A, B and C, each of which is manufactured on a different machine. The length of section A, in inches has a normal distribution with mean 20 and variance 0.04. The length of section B, in inches, has a normal distribution with mean 14 and variance 0.01. The length of section C

### Probability based on normal distribution.Normal probability problems

Suppose that the annual rate of return for a common biotechnology stock is normally distributed with a mean of 5.5% and a standard deviation of 6% . Find the probability that the one-year return of this stock will be positive.

### Consider a random variable, z, that has a standardized normal distribution. Determine the following probabilities: Bowser Bites Industries (BBI) sells large------standard deviation of 1.25 kilograms. What is the probability that a filled bag will weigh less than 49.5 kilograms?

Can you please assist with questions 6-11 and 6-17 putting the answers and solutions in an excel spread sheet. 6.11 ) Consider a random variable, z, that has a standardized normal distribution. Determine the following probabilities: a) P(0<z<1.96) b) P(z>1.645) c) P(1.28<z<2.33) d) P(-2<z<3) e) P(z>-1) 6.17 ) Bow

### Problems with Normal Distribution

Amazing Bakers sells bread to 40 supermarkets. It costs Amazing \$1,250 per day to operate its plant. The profit per loaf of bread sold in the supermarket is \$.025. Any unsold bread is returned to the Amazing Thrift Store to be sold at a loss of \$.015. a. If sales follow a normal distribution with µ = 70,000 and &#61555; =

### Coin flip Probability: Gaussian distribution

See attached file. A coin is flipped. If the outcome is heads you draw a number form a Gaussian distribution with mean 0 and variance 1. If the outcome is tails you draw a number from a uniform [0,1] distribution. What is the mean and variance of the distribution for the number you will generate?

### Internet hookup, insurance spending, 3 songs, home loans

1. Customers experiencing technical difficulties with their internet cable hook up may call 800 numbers for technical support. It takes the technician between 30 second to 10 minutes to resolve the problem. The distribution of this support time follows the uniform distribution. a. what are the values for a and b in minutes?

### Multiple choice questions and answers

Suppose a population consisted of 20 items. How many different samples of n = 3 are possible? A. 1140 B. 6840 C. 20 D. 120 The difference between the sample mean and the population mean is called the A. Population standard deviation. B. Population mean. C. Standard error of the mean. D. Sa

### Normal Distribution: Tax Preparation Fees

In 1999, the average charge for tax preparation by H&R Block, Inc. was \$84.57. Assuming a normal distribution and a standard deviation of o = \$10, what proportion of H&R Block's tax preparation fees were. a. more than \$84.57? b. between \$64.57 and \$104.57? c. between \$74.57 and \$94.57? d. more than \$104.57?

### Random Sampling: Determining Mean Amount of Life Insurance

Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is \$110,000. This distribution follows the normal distribution with a standard deviation of \$40,000. a. If we select a random sample of 50 households, what is the standard error of the mean? b.

### Normal Probabilities: Serum Cholesterol Levels in Men

You may find the probabilities using the Table or software of your choice. Please explain how you obtained your results. The serum cholesterol levels in men aged 18-24 are normally distributed with a mean of 178.1 and a standard deviation of 40.7. Units are mg/100 mL, and the data are based on the National Health Survey.

### Standard Error of the Mean vs. Standard Deviation

When we move from the basic normal distribution to the sampling distribution of the mean we substitute the standard error of the mean for the standard deviation when we make the conversion to the standardized normal distribution. Why do we use the standard error of the mean in this case? And how does using the standard error aff

### Various Stats Questions with Explanations

1) Describe how scale impacts the interpretation of a graph 2) Name the lowest number of a statistically significant sample size 3) State the statistically appropriate percentage total of displays 4) Explain how mean, median, and mode are applied to categorical and numerical data 5) List the characteristics of a normal bell

### An expert response to: Normal Probability

Chapter 7, problem 37 - The net sales and the number of employees for aluminum fabricators with similar characteristics are organized into frequency distributions. Both are normally distributed. For the net sales, the mean is \$180 million and the standard deviation is \$25 million. For the number of employees, the mean is 1,500 a

### Use of the normal curve

What is the significance and use of the normal curve. How can the normal curve related to a real world situation?

### Temperature Readings and Normal Distribution

If the reading of the thermometer is normally distributed with a mean 0.0 C and a standard distribution of 1.0 C, find the probability that a reading is: a. Between 0.0 and (0.04)n C b. Less than (-0.04n) C