# Question

A variable is said to be uniformly distributed or to have a uniform distribution with parameters a and b if its distribution has the shape of the horizontal line segment y = 1/(b − a), for a < x < b. The mean and standard deviation of such a variable are (a + b)/2 and (b − a)/√ 12, respectively. The basic random-number generator on a computer or calculator, which returns a number between 0 and 1, simulates a variable having a uniform distribution with parameters 0 and 1.

a. Sketch the distribution of a uniformly distributed variable with parameters 0 and 1. Observe from your sketch that such a variable is far from being normally distributed.

b. Use the technology of your choice to simulate 2000 samples of two random numbers between 0 and 1.

c. Find the sample mean of each of the 2000 samples obtained in part (b).

d. Determine the mean and standard deviation of the 2000 sample means.

e. Theoretically, what are the mean and the standard deviation of all possible sample means for samples of size 2? Compare your answers to those you obtained in part (d).

f. Obtain a histogram of the 2000 sample means. Is the histogram bell shaped? Would you expect it to be?

g. Repeat parts (b)-(f) for a sample size of 35.

a. Sketch the distribution of a uniformly distributed variable with parameters 0 and 1. Observe from your sketch that such a variable is far from being normally distributed.

b. Use the technology of your choice to simulate 2000 samples of two random numbers between 0 and 1.

c. Find the sample mean of each of the 2000 samples obtained in part (b).

d. Determine the mean and standard deviation of the 2000 sample means.

e. Theoretically, what are the mean and the standard deviation of all possible sample means for samples of size 2? Compare your answers to those you obtained in part (d).

f. Obtain a histogram of the 2000 sample means. Is the histogram bell shaped? Would you expect it to be?

g. Repeat parts (b)-(f) for a sample size of 35.

## Answer to relevant Questions

a. What percentage of the waybills constituted the sample? b. What percentage error was made by using the sample to estimate the total revenue due C&O? c. At the time of the study, the cost of a census was approximately ...Comerica Bank publishes information on new car prices in Comerica Auto Affordability Index. In the year 2007, Americans spent an average of $28,200 for a new car (light vehicle). Assume a standard deviation of $10,200. a. ...The subterranean coruro (Spalacopus cyanus) is a social rodent that lives in large colonies in underground burrows that can reach lengths of up to 600 meters. Zoologists S. Begall and M. Gallardo studied the characteristics ...An issue of Scientific American revealed that the batting averages of major-league baseball players are normally distributed with mean .270 and standard deviation .031. a. Simulate 2000 samples of five batting averages ...In developing Procedure 8.1, we assumed that the variable under consideration is normally distributed. a. Explain why we needed that assumption. b. Explain why the procedure yields an approximately correct confidence ...Post your question

0