Math Answers

For a continuous random variable that has a normal distribution with mean of 24 and a standard deviation of 6, find the area under the normal curve from 𝑥=18 and 𝑥=21.

A population and = 6 consists of the following values: 12, 14, 16, 18, 20 and 22. Estimate the population mean by using a sampling distribution with a random variable of size n= 3. Prepare and analyze the probability distributions of the sample means of the population values of N = 6.

Suppose that the relation consists of the scores of 6 students in a certain examination as follows 9, 11, 13, 15, 17 and 19 using the sampling distribution is to make the population mean using a random variable of the size n = 2.

Let X be a random variable with pdf

𝑓(𝑥) = {

2(1 + 𝑥)

27 𝑖𝑓 2 ≤ 𝑥 ≤ 5

0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Find (i) 𝑃(𝑋 < 4) (ii) 𝑃(3 < 𝑥 ≤ 4)

The density function of sheer strength of spot welds is given by

𝑓(𝑥) = {

𝑥/ 160000 𝑓𝑜𝑟 0 ≤ 𝑥 ≤ 400

800 − 𝑥/ 160000 𝑓𝑜𝑟 400 ≤ 𝑥 ≤ 800

Find the number a such that 𝑃(𝑋 < 𝑎) = 0.50

student is to match three historical events (Mahatma Gandhi’s Birthday, India’s freedom, 

and First World War) with three years (1947, 1914, 1896). If he guesses with no knowledge 

of the correct answers, what is the probability of the number of answers he gets correctly?

Suppose the population consists of the scores of 6 students in a certain examination, as follows: 9, 11, 13, 15, 17 and 19. By using the sampling distribution, estimate the population mean using a random variable of the size n=2.

Suppose the population consists of the scores of 6 students in a certain examination, as follows: 9, 11, 13, 15, 17, and 19 . Byusing the sampling distribution, estimate the population mean using a random variable of the size n=2

Activity IV CHECK WHAT YOU KNOW. Solve the following problems. (2 points each)

1. Given n = 12; = 120 ml;s = 6. The parent population is normally distributed.

Find:

a. The point estimate.

b. The interval estimate of mean.

2. Rochelle wants to know the mean of all entering trainees in a boot camp. The mean age of a

random sample of 25 trainees is 18 years and the standard deviation is 1.3 years. The sample

comes from normally distributed population. Use a = 0.1 to find the following:

a. The point estimate.

b. The error.

c. The interval estimate of the population of the mean.

3.b. The top-selling Amar tire is rated 70,000 KMs, which means nothing. In fact, the distance

the tires can run until they wear out is a normally distributed random variable with a mean

of 82,000 KMs and a standard deviation of 6,400 KMs.

What is the probability that a tire wears out before 70,000 KMs?

What is the probability that a tire lasts more than 100,000 KMs?

Note: You may use Z-table for this.

Z-table link- Normal Table.xls (5 Marks)

Solve by method of variation of parameters.

d^y/dx^2 + dy/dx + 1 = e^x