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# Normal Distribution

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### Sampling Distribution and Test Proportion

Use the following information for problems 1-3. Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance using the given sample statistics. 1. Claim: p > 0:30; = 0:05. Sample statistics: p^ = 0:35, n = 50. 2. Claim

### Statistics Problem: Interference

Suppose Z and V are two independent random variables, Z has the normal distribution with expected value 0 and variance 1 and V = 1 or -1, each with probability 0.5. Let Y = ZV. a. Derive the distribution of Y. b. Find the covariance of Y and Z. c. Are Y and Z independent? Justify your answer.

### Statistics Problem: Effective Manufacturing Adjustments

The data in the attachment provides two random samples from two successive days runs of a product. You adjusted the manufacturing process after the first day in an attempt to decrease the mean value. Using interval estimates, to a 95% confidence level, was your most recent adjustment effective?

### Statistics: Normal Distribution Question

Hi, I need an explanation on how to solve this? I really do not understand these concepts. Question: The average customer waiting time at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager installs a new system and checks if the use of the new system will decrease av

### Statistics: The Normal Distribution and Standard Deviation

Below are questions regarding the weight of football players in the NFL. I need assistance in figuring out the following questions. 1. The weight of football players in the NFL is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. What is the probability that a randomly selected football

### Standard Deviation and Normal Distribution

A major department store has determined that its customers charge an average of \$500 per month, with a standard deviation of \$80. Assume the amounts of charges are normally distributed. a. What percentage of customers charges more than \$380 per month? b. What percentage of customers charges less than \$340 per month? c. What p

### Statistics: Normal Distribution and Standard Deviation

Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6. a. What is the probability that a randomly selected exam will have a score of at least 71? b. What percentage of exams will have scores between 89 and 92?

### Population and Standard Mean

1. Assume the population standard deviation is a=25. (The a is actually the funny looking 0 with the line that goes from the top right up at an angle) Compute the standard error of the mean O (funny o with line) line over x, for sample sizes of 50, 100, 150, and 200. What can you say about the size of the standard error of the m

### Find the joint distribution of X and Y

A point is generated at random in the plane according to the following polar scheme. A radius R is chosen, where the distribution of R^2 is qui-square with 2 degrees of freedom. Independently, an angle theta is chosen, where theta ~ uniform(0, 2 pi). Find the joint distribution of X = R cos theta and Y = R sin theta.

### Test the Claim that P1 = P2

Use a significance level of alpha = 0.05 to test the claim that P1 = P2. Use the given sample sizes and numbers of successes to find (a) the pooled estimate p, (b) the z test statistic, (c) the critical z-values, and (d) the P-value. Treatment Group: n1 =280 X1 = 70 Placebo Group: n2 = 450 X2 = 90

### Statistics: Using the Wrong Distribution

Using the wrong distribution: When testing a claim about a population mean with a simple random sample selected from a normally distributed population with unknown standard deviation of all values in a population, the student t distribution should be used for finding critical values and/or a p-value. If the standard normal dist

### Simulation with Random Numbers.

Simulate 10000 of X and Y random variables using excels Data Analysis package where both X and Y are normal with mean = 20 and standard deviation = 5. Show, using simulations, that the variables Z= min(X,Y) and W=max(X,Y) are NOT normally distributed. Y any interest?C

### Distributions/Frequency

What is the purpose of developing a frequency distribution? What is the relationship between the relative frequency and the cumulative frequency? Could a frequency distribution contain qualitative data? Why? Describe the properties of a normal distribution. Why are there infinite possible normal distributions? Why should one

### Normal Distribution and Standard Deviation Analysis

The resting heart rate for a sample of people are normally distributed with a mean of 70 and a standard deviation of 15. Use 68-95-99.7 rule to find the % of heart rate in each of the following categories: less than 55 less than 40 less than 85 less than 100 greater than 85 greater than 55 greater than 40 between 55 and

### Risk Analysis Question

In performing a symmetric approximation, you calculate a mean of the total system cost as \$1,725K. The variance is 22500. The POE is \$1,600K. What is the probability of overrunning the POE? 50.56% 29.67% 83.33% 79.67%

### Mean, Standard Deviation, and Normal Distribution

If the mean exam score in a class of 30 students is an 80 out of 100 and the standard deviation on the exam is 15, what percentage of students earned between 65 and 95, assuming a normal distribution of grades on the exam? How alarmed should a student with a score of 49 be with his grade?

### Weights of Water Taxi Passengers

When a water taxi sank in the Baltimore Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lbs. It was also noted that the mean weight of a passenger was assumed to be 140 lbs. Assume a "worst case" scenario in which all the passengers are adult men. (This could easily occur in a

### Finding Area Under the Standard Normal Distribution Curve

1.)The average monthly mortgage payment including principal and interest is \$982 in the United States. If the standard deviation is approximately \$180 and the mortgage payments are approximately normally distributed, find the probability that a randomly selected monthly payments is: A. More than \$1000 B. More than \$1475 C. B

### Quantitative Reasoning for Business: Frequency distribution, normal distribution, mean, median and mode

What is the purpose of developing a frequency distribution? What is the relationship between the relative frequency and the cumulative frequency? Could a frequency distribution contain qualitative data? Why? Describe the properties of a normal distribution. Why are there infinite possible normal distributions? Why should one

### The Empirical Rule For Statistics Students

For a normal distribution curve with a mean of 19 and a standard deviation of 6, which range of the variable defines an area under the curve corresponding to a probability of approximately 99.7%? a. from 1 to 37 b. from 13 to 25 c. from 19 to 31 d. from 7 to 31

### The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of bulbs has lifetimes that lie within 1 standard deviation of the mean on either side?

### Calculating Standard Normal Probability Distribution

Solve the following: 1. Assume that the thermometer readings are normally distributed with a mean of 0Â° C and a standard deviation of 1.00Â° C. A thermometer is randomly selected and tested. For each case given below, draw a sketch and find the probability. The given values are in Celsius degrees. [Note: If using a calculator

### Normal Modelling of IQ Test Scores

I find this question really difficult to answer and I need help formulating a response. Some IQ tests are standardized to a normal model with a mean of 100 and a standard deviation of 16. a. Draw a model for these IQ scores, clearly label it , showing what the 65-95-99.7 rule predicts about the score. b. In what interv

### Normal Distribution Curve/Chart Statistics

I need to know how to solve this question using the normal distribution curve / chart and how to answer using Excels Fx statistics function The first statistics exam had a mean of 65 and a standard deviation of 10 points; the second had a mean of 80 and a standard deviation of 5 points. Derrick scored an 80 on both tests. Jul

### Calculate mean, standard deviation and check normal distribution

0.4 0.8 0.6 7.2 5.8 -1.5 12.2 0.8 0.6 0.9 -0.4 5.7 4.1 7.9 12.8 3.4 0.8 3.2 7 14.9 -1.7 -0.4 6 0 0.1 15.8 11.7 4.6 -0.1 4.8 3.7 -1.2 14.4 7.6 11.4 3.6 -0.5 5

### Standard Score: Normal Distribution

Consider a normal population with mu = 25 and sigma = 7.0. (A) Calculate the standard score for a value x of 26 (B) Calculate the standard score for a randomly selected sample of 30 with = 26 (C) Explain why the standard scores of 26 are different between A and B above

### Normal and Curved Distributions

A) Discuss the concept of the normal distribution, why it is important, and what you think it means. B) When students talk about "grading on the curve," how does that apply to the normal distribution?

### Why do we use standard deviation? Why do we use averages?

Define standard deviation. Define mathematical averages. Why is the standard deviation less than the mathematical average? Why do we use standard deviation? Why do we use a mathematical average?

### Statistics Problem for standard normal distribution

1. 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 random and finding the customer charged between \$70 and \$83?

### Multivariate normality test in SPSS

Please SAVE the attached file and open on SPSS to see the graph.(dat file) The data attached in file consists of a 100 observations and 5 variables. Evaluate the assumption that the data was sampled from the multivariate normal distribution.