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# Normal Distribution

### In its standardized form, the normal distribution

1. In its standardized form, the normal distribution a) has a mean of 0 and a standard deviation of 1. b) has a mean of 1 and a variance of 0. c) has an area equal to 0.5. d) cannot be used to approximate discrete probability distributions. 2. For some positive value of Z, the probability that a standard normal variable

### Normal probability distribution characteristics

Which of the following is not a characteristic of the normal probability distribution? a. It is a discrete probability distribution. b. The total area under the curve is always equal to 1 c. 68% of the area under the normal curve is within one standard deviation of the mean. d. A negative z value is to the

### Assume that the population of heights of male college students is approximately normally distributed

1. Assume that the population of heights of male college students is approximately normally distributed with mean m of 68 inches and standard deviation s of 3.75 inches. A random sample of 16 heights is obtained. Find the proportion of male college students whose height is greater than 70 inches. 2. The diameters of oranges i

### A recent study found that the average life expectancy of a person living in Africa is 53 years with a standard deviation of 7.5 years.

A recent study found that the average life expectancy of a person living in Africa is 53 years with a standard deviation of 7.5 years. If a person in Africa is selected at random, what is the probability that the person will die before the age of 65? a. 94.52% b. 82.89% c. 94.95% d. 88.49%

### Normal Distribution - Sheet Metal Stamping Machine

For the sheet-metal stamping machine in a certain factory, the time between failures, X1 has a mean between the failures, of 56 hours and a variance of 16 hours. The prepair time X2, has a mean time to repair of 5 hours and a variance of 4 hours. a) If X1 and X2 are independent , find the expected value and the variance of Y

### Normal Distribution - Confidence Limits

The mean amount of a purchase at the Smith Hardware store is \$23.50 with a standard deviation of \$5.00. The amounts purchased follow a normal distribution. 50 customers were sampled: a.What is the likelihood the sample mean is at least \$25.00? b.What is the likelihood the sample mean will fall into the \$22.50 to \$25.00 range

### Probability Percentage: Normal Distribution & Standard Deviation

According to a retail electronics chain, adults in the 40 to 50 year old age group, the mean amount spent per year on electronics is \$1998. Assume that the amount spent follows a normal distribution with a standard deviation of \$550. a. What percent of adults in this age group spend more than \$2500 per year on electronics? b

### What does it mean to say that x = 152 has a standard score of +1.5?

A. What does it mean to say that x = 152 has a standard score of +1.5? b. What does it mean to say that a particular value of x has a z-score of -2.1? c. In general, what is the standard score a measure of? 6. An animal trainer obtained the following data (Table A) in a study of reaction times of dogs (in seconds) to

### The mean weight of loads of rock is 46.0 tons with a standard deviation of 8.0 tons.

The mean weight of loads of rock is 46.0 tons with a standard deviation of 8.0 tons. If 25 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 44.24 tons. Assume that the variable is normally distributed. a. 0.1677 b. 0.1357 c. 0.4129 d. 0.2957

### Normality Assumptions of Populations

I have completed the problem. But I am knowing how to check the normality assumptions of both population. I used minitab for output. Lesson 10, Practice Problems 1. Problem 6.8: First check assumptions by verification that there are both (1) independent samples from the two populations and (2) that data in each sample are

### TESTS OF THE EQUALITY OF TWO NORMAL DISTRIBUTIONS

Please see the attached file. If you have any question or suggestion on my posting, please let me know. Thank you. --------------------------- (The material is from TESTS OF THE EQUALITY OF TWO NORMAL DISTRIBUTION. Please use technological device to solve/draw if you need (preferably Excel or Mathematica), please expla

### (a) P(x > 74) in a normally distributed set of data with a mean of 62 and a standard deviation of 9 ... and 3 other questions

A) P(x > 74) in a normally distributed set of data with a mean of 62 and a standard deviation of 9. b) P(49 < x < 78) in a normally distributed set of data with a mean of 62 and a standard deviation of 9. c) The amount of annual snowfall in a certain mountain range is normally distributed with a mean of 109 inches, and

### Weekly Salaries of Teachers: Normal Distribution

The weekly salaries of teachers in one state are normally distributed with a mean of \$490 and a standard deviation of \$45. a. What is the probability that a randomly selected teacher earns more than \$525 per week? b. What is the probability a randomly selected teacher earns less than \$435 per week?

### The mean amount of gasoline and services charged by Key Refining Company credit customers is \$70 per month.

Dear OTA, Help me with the attached Problems. Thanks 13. The mean amount of gasoline and services charged by Key Refining Company credit customers is \$70 per month. The distribution of amounts spent is approximately normal with a standard deviation of \$10. What is the probability of selecting a credit card customer at rando

### Quality Check on Water Bottle Volume

An airline serves bottles of Galena Spring Water that are supposed to contain an average of 10 ounces. The filling process follows a normal distribution with process standard deviation 0.07 ounce. Twelve randomly chosen bottles had the weights shown below (in ounces). (a) Set up a two-tailed decision rule to detect quality c

### Sample Sizes, Normal Distribution, and T-Distribution

1. In order to efficiently bid on a contract, a contractor wants to be 99% confident that his error is less than two hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the population standard deviation o- is 4.5 hours. Find the minimum sample size "n" that is needed to estima

### Binomial Probability and Confidence Intervals

(17) A recent study following attrition rates at a major university has shown that 43% of all incoming freshmen do not graduate within 4 years of entrance. If 200 freshmen are randomly sampled this year and their progress is followed, what is the probability that 100 or less will not graduate within the next 4 years. Verify that

### Daily output of Marathon's Garyville, Lousiana, refinery is normally distributed with a mean of 232,000 barrels of crude oil per day with a standard deviation of 7,000 barrels.

Daily output of Marathon's Garyville, Lousiana, refinery is normally distributed with a mean of 232,000 barrels of crude oil per day with a standard deviation of 7,000 barrels. (a) What is the probability of producing at least 232,000 barrels? (b) Between 232,000 and 239,000 barrels? (c) Less than 239,000 barrels? (d) Less than

### Variables and Normal Distribution

Discuss why you would or would not expect each of the following variables to be normally distributed. Hint:Would you expect a single central mode and tapering tails? Would the distribution be roughly symmetric? Would one tail be longer than the other? a. Shoe size of adult males. b. Years of education of 30-year-old employed

### A Discrete and A Continuous Random Variable

Explain the difference between a discrete and a continuous random variable. Give two examples of each type of random variable. Determine whether each of the distributions given below represents a probability distribution. Justify your answer. a) x 1 2 3 4 P (x) 1/8 1/8 3/8 1/8 b) x 3 6 8

### The Normal Curve of Distribution: Definition, Shape, Formula

How would you define the normal curve of distribution? Why do you think the normal curve of distribution is a bell shape? Can you please describe and explain the formula for the normal curve of distribution? Also explain the process of hypothesis testing in research creation of hypothesis testing for problem statements, vali

### The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds.

Please annotate steps when solving the attached problems. I would like to use them as a reference. Thanks The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. a. What is the area between 415 pounds and the mean of 400 pounds? b. What is the area between the mean and 395 pounds? c. Wha

### Z-Scores and Normal Distribution

A study of long distance phone calls made from the corporate offices of the Pepsi Bottling Group, Inc., in Somers, New York, showed the calls follow the normal distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minutes. a. What fraction of the calls last between 4.2 and 5 minutes?

### Defining the Normal Curve of Distribution

I have been given the task to study a group of students that are completing their BA degree in psychology. The main purpose of the study is to find out their level of satisfaction and to identify the most helpful areas provided by the program. Based upon this information formulate: Formulate hypothesis for this problem. I

### Online professor's response to: normal distribution

Always get overwhelmed by the amount of material when covered at a comprehensive level. Attached is the study material of what to be prepared to cover at the conclusion of this course. I have worked through them but get stumped at several points. Can you provide a systematic approach to these problems and provide a reference to

### Describe the Properties of a Normal Distribution

Describe the properties of a normal distribution. Explain why there are an infinite number of normal distributions. Why do we want to assume that our sample data represent a population distribution?

### Some IQ scores are standardized with a mean of 100 and a standard deviation of 16.

Some IQ scores are standardized with a mean of 100 and a standard deviation of 16. Using the 68-95-99.7 Rule, Determine: a. In what interval you would expect the middle 95% of the IQ scores to be found. b. What percent of people would have an IQ score above 116. c. What percent of people would have an IQ score 68 and 84.

### Tire Manufacturing: Normal Distribution and Standard Deviation

A tire manufacturer believes that the tread life of its snow tires can be described as a normal distribution with a mean of 32,000 miles and a standard deviation of 2500 miles. a. If you buy a set of these tires, would it be reasonable to expect they will last 40,000 miles? What do you base your decision on? b. What perce

### Probability calculation Using Normal Distribution Problem

Please help with the following question. Provide step by step calculations. Assume that the number of calories in a McDonald's Egg McMuffin is a normally distributed random variable with a mean of 290 calories and a standard deviation of 14 calories. (a) What is the probability that a particular serving contains fewer than 3

### Normal Distribution Standards

Find the standard normal area for each of the following, showing your reasoning clearly and indicating which table you used. a. P(1.22 < Z < 2.15) b. P (3.00 < Z < 2.00) c. P (Z < 2.00) d. P(Z = 0)