Statistics and Probability Answers

A population consist of five measurements 2,6,8,3&1. How many different samples of size n=2 can be drawn from the population? What is the mean & variance of the sampling distribution of the sample means?

A university has analyzed the results of 1,000 students after the first year examinations. The result of the analysis is summarized below

 Types of sponsorship

Examination results

Government

Private

Church

Students who were to be discontinued

155

150

105

Students who passed the examination

180

195

170

Students who were to sit for a supplementary paper

20

5

20

     Required

The probability that a student was discontinued or was required to sit for a supplementary

Find the corresponding area between z = 0 and each of the following: a. z = 0.96 b. z = 2.74 c. z = -1.67

1.z=2

2.z=3.1

if two varieties are tested in 5 different locations for their yeld proformance in (q/ha) with the follo results.Find out which variety which is more consistent over the location by comparing their CV value?

Variety A -12,8,10,11,14

Variety B - 15,9,7,12,12

From a population of 700 plants, 500 plants are healthy, rest are unhealthy. For a sample size of 10 plants, calculate the probabilities that—(a) Exactly 3 are unhealthy (b) at least 3 plants are unhealthy (c) at most 3 plants are unhealthy (d) Exactly 3 are healthy (e) None healthy?

Calculate the mean and the variance of the discrete random variable X which can take only values 1, 2, and 3, given that P(1) = 10/33, P(2) = 1/3, and P(3) = 12/33.

P(X) X-P(X) X²P(X)

Solve for the mean and the variance of the discrete random variable X which can take only the values 2, 4, 5 and 9, given that P(2) = 9/20, P(4) = 1/20, P(5) = 1/5 and P(9) = 3/10.

X P(X) X∙P(X) X2∙P(X)

Experiment: Tossing two coins. Random variable 𝑋 = number of heads a) List all possible sample space. b) Find the random variable values. c) Find the probabilities for the random variable values.

You play a game with two six-sided dice. If you roll a sum of 5 or 7, you win ₱400. If you

roll a sum of 6 or 8, you win ₱300. If you roll a sum of 11 or 12, you win ₱200. However,

you lose ₱250 for anything else. If you continue to play the game, how much do you

expect to win or lose in the game? Will you encourage your friend to play that kind of

game? Why or why not?

The officers of the Mathematics Club are planning to sell 280 tickets to be raffled during

the school’s foundation day. One ticket will win ₱5,000, two tickets will win ₱3,000, three

tickets will win ₱2,000 and the other tickets will win nothing. If you will buy one ticket,

what will be your expected value and variance of his gain?