Statistics and Probability Answers

1) The jdf of the random variables X, Y is given as

f(x, y) = { 2 /5 (2x + 3y), 0 < x < 1, 0 < y < 1

0, elsewhere

find Pr [ 1 /3 < X < 2 /3 |y > 3 /4 ]

A population consists of the four measurements as follow:

5 9 10 8

What is the mean and standard deviation of the population?

In a recent survey of 1159 students, 968 of them would like to recommend a website to their friends. Construct a 95% confidence interval to estimate the proportion of all students who would recommend the website to their friends.

Give your answers to three decimals:

_____,_____

A survey of 98 randomly selected students finds that they spend a mean of $435 per semester. Assume that the population standard deviation is $56 per month.

Confidence Interval: What is the 95% confidence interval to estimate the population mean? (Round your answers to two decimal places.)

______ < u < _______

For a normal distribution, assume the 'sample' standard deviation is 8. What is the maximal margin of error associated with a 99% confidence interval for the true population mean if n = 25. ?

(Round to two decimal places)

What is the t value with a 90% confidence interval for the true population mean if the sample size n = 27?

(Please keep three decimal places)

t value= ____________

Perpetrators of a crime who have been given the maximum sentence of 10 years are

believed bya fiscal to have been sentenced to no more than 7 years on the average.

random sample of 20of these crime offenders reveals a mean sentence of 7.6 years with a

standard deviation of 2.4 years. Is the fiscal correct in his suspicions at the 0.05 level of

significance?

Step:

1. State the null and alternative hypothesis

concerning the population mean, "\\mu" and the type of test to be used.

2.Specify the level of significance "\\alpha"

3.State the decision rule

4. Collect the data and perform calculations.

5. Make a statistical decision.

6.State the conclusion

A group of students got the following scores in a test; 5, 10, 15, and 25. Consider samples of size 2 that can be selected from the population. What is the mean of the population?

Work Interruptions Survey found that out of 300 workers, 245 said they were interrupted three or more times an hour by phone messages, faxes, etc. Find the 90% confidence interval of the population proportion of workers who are interrupted three or more times an hour.