Math Answers

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

An element with mass 290 grams decays by 13.2% per minute. How much of the element is remaining after 14 minutes, the nearest of a gram?

By examining the determinant of the coefficient matrix, show that the following system has a nontrivial solution if and only if α = β

x + y + αz = 0

x + y + βz = 0

αx + βy + z = 0

If the characteristic polynomial of a matrix A is p(λ) = λ²+ 1, then A is invertible

An n x n matrix with fewer than n distinct eigen values is not diagonalizable

Define the following theorems with respect to a random vector

i) Central limit theorem

ii) Weak law of large numbers

inverse of 1 2 3

4 5 3

7 8 9

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.)

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