Statistics and Probability Answers

Based on past experience, it is assumed that the number of flaws of per metre in rolls of wrapping paper follows a Poisson distribution with a mean of 2 flaws per 4 metres of paper. The probability (correct to 2 decimal places) that more than 2 flaws will be observed in 5 metres of wrapping paper produced is:

A random sample of 11 observations was taken from normal population. The sample mean and

standard deviation are 74.5 and 9 accordingly. Can we infer at 5% significance level that the

population mean is greater than 70?

5. Repeat number 4 with assuming the population standard deviation = 9

Define the following theorems with respect to a random vector

i) Central limit theorem

ii) Weak law of large numbers

Question 2 [25] Suppose that the latest census indicates that for every 10 young people available to work only 4 are employed. Suppose a random sample of 20 young graduates is selected. Required: a) What is the probability that they are all employed? b) What is the probability that none of them are employed? c) What is the probability that at least four are employed? d) What is the probability that at most fifteen are employed? e) What is the probability that the number of young graduates who are employed is greater than ten but less than fifteen? f) What is the expected number of graduates who are not employed? g) What is the standard deviation for the number of graduates who are not employed?

Assume that X has a uniform distribution over [0; 1] and that Y has the uniform distribution over

[2; 3]: Which of the following statements are true and which are false? Justify your answers!

(a) P (X < Y) = 1.

(b) Since X is smaller than Y , P (X < 1) > P (Y < 1).

(c) There are some values a for which P (X < a) = P (Y < a).

survey of 31 randomly selected students finds that they save a mean of $82 per semester by

using a website. Assume the date comes from a normal distribution and the sample standard deviation is $18 per month.

Confidence Interval: What is the 99% confidence interval to estimate the population mean? (Round your

answers to two decimal places.)

____< u < _____

A sample of 25 women had a variance in IQ scores of 62. A sample of 18 men had a variance of 72. Do the women have a smaller variance in IQ scores at the 0.01 level of significance? Assume both populations are normally distributed

A researcher claims that 10 year olds watch 6.6 hours of TV daily with SD = 2.5 hours. You try to verify this with the following sample data of 100 and a sample mean of 6.1 hours. Test the claim of the researcher. Test at α = .01

A Research Director of a certain university wants to replicate the result of the study 10 years ago with a standard deviation of 0.14. He wants to estimate the population mean to within an error of 0.04 of its true value. Using 95% confidence level, what is the sample size that he needs?

The joint probability density of X, Y is

f(x, y) = e ^{−(x + y)} xi > 0 i = 1, 2

0 otherwise

Using the change of variable technique, determine the joint distribution of Z = X and W = X + Y