Explore BrainMass

# Normal Distribution

### 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?

### Population Distribution Probabilities

A population distribution is normal with a mean of 25 and a standard deviation of 5. If a piece of datum is randomly taken from this distribution, what is the probability that it is less than 20? If a sample of 4 pieces of data are taken from this distribution, what is the probability that the mean will be less than 20?

### 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)

### Question about Normal Distributions and Z-Scores

Assume that the average annual salary for a worker in the United States is \$27500 and that the annual salaries for Americans are normally distributed with a standard deviation equal to \$6250. Find the following: a) What percentage of Americans earn below \$18000? b) What percentage of Americans earn above \$40000?

### Solving a Normal Distribution Problem

What are the characteristics of the normal distribution? Why is the normal distribution important in statistical analysis? Provide an example of an application of the normal distribution.

### Z-Scores, Percentile, and Normal Distributions

The diameters of oranges in a certain orchard are normally distributed with a mean of 5.26 inches and a standard deviation of 0.50 inches. a. What percentage of the oranges in this orchard have diameters less than 4.5 inches? b. What percentage of the oranges in this orchard is larger than 5.12 inches? c. A random sample

### Bivariate Normal Distributions

Please see the attached file for the fully formatted problems.

### v

Federal Government conducts 86,991 pre-employment tests on job applicants engaged in safety and security-related jobs and found that 1,143 were positive. a) Construct 95% confidence interval for population proportion of positive drug tests. b) Why is the the normality assumption not a problem, despite the small value of p?

### Normal Distribution - Motorcycles

When you compare the lengths of motorcycles you find the mean to be 65" and the standard deviation is 2.5". You discover your motorcycle is longer than 80% of the motorcycles. How long is your motorcycle?

### Standard Normal Random Variable

Figure the value of c p(c is less an or equal to z which is equal to or less than .99)=.8197

### Description of standard normal random variable

Let z be a standard normal random variable and calculate the following probabilities: p(z is greater than .73) = p(z is less than or equal to 1.75 = p(-1.33 is less than z which is less than 2.2) =

### Sampling Distribution of the Sample

Please answer and fully explain the below question: Under what condition, if any, is it not possible for us to assume that the sampling distribution of the sample mean is approximately normally distributed?

### Normal Approximation and Binomial Probability

Please help with the following problem. Past experience indicates that 30% of all individuals entering a certain store decide to make a purchase. Using (i) the binomial distribution and (ii) the normal approximation to the binomial, find that probability that 10 or more of the 30 individuals entering the store in the given h

### Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean \$25 and standard deviation \$8.

Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean \$25 and standard deviation \$8. a) What is the probability that a randomly selected customer spends less than \$35 at this store? b) What is the probability that a randomly selected custome

### Normal Distribution: Orders Being Shipped

On average, your department ships an order two hours after it is received. The distribution of times is approximately normal, the standard deviation is 15 mins. -today you handled 120 orders (empirical rule)a. how many orders would you expect to be shipped: within 2 hours of being received --b. within 1 hour 30 mins How many

### Probability Statements and Regression Data

See the attached file. 3. Spring-loaded canons are designed to shoot t-shirts into the stands at sporting events. Test firings are conducted on a large level field. The distance that a t-shirt flies is a function of the angle of elevation. When the angle is 35 degrees, the distances follow a normal distribution with a mean of