Statistics and Probability Answers

Question 7. There are 40 students in the Statistics class; of them, 15 are girls and 25 are boys. The teacher wants to select randomly a group of ten for a volunteer activity. What is the probability of making the volunteer group with 5 girls and 5 boys? *

What is the probability that no more than 156 U.S adults of the 240 surveyed believe solar energy is very effective in minimizing air pollution?

Suppose X and Y are random variables with P(X = 1) = P(X = -1) = 12; P(Y = 1) = P(Y = -1) = 1
Let c = P(X = 1 and Y = 1).
(a) Determine the joint distribution of X and Y, Cov(X, Y), and Cor(X, Y).
(b) For what value(s) of c are X and Y independent? For what value(s) of c are X and Y 100% correlated?

A market research company informs a prospective mini marker entrepreneur that the average income per household in the region is RM60 000 per annum. The household income is assumed to be normally distributed with standard deviation of RM7000, based on an early study. For a random sample of 130 households, the mean household income is found to be RM47 000. Test the null hypothesis that the population mean household income is RM60 000 at 5 percent significance level.

A test at the 5% significance level, weather the single sample values of 82 comes from a normal population with mean 70 and variance 54.
Explain your answer.

An important practice is to check the validity of any data set that you analyze. One goal is to detect typos in the data, and another would be to detect faulty measurements. Recall that outliers are observations with values outside the “normal” range of values of the rest of the observations.

Specify a large population that you might want to study and describe the type numeric measurement that you will collect (examples: a count of things, the height of people, a score on a survey, the weight of something). What would you do if you found a couple outliers in a sample of size 100? What would you do if you found two values that were twice as big as the next highest value?

You may use examples from your area of interest, such as monthly sales levels of a product, file transfer times to different computer on a network, characteristics of people (height, time to run the 100 meter dash, statistics grades, etc.), trading volume on a stock exchange, or other such things.

Analyse the variance in Latin square of yields (in quintels) of wheat where A,B,C,D represent the different manures used .
D222
A221
C223
B222

B224
C223
A222
D225

A220
B219
D220
C221

C222
D223
B221
A222

Test whether the different manures used have given significantly different yields.

1. Matteo and Amber have invented a two-player game:
• For each turn, both players roll a die.
- Player 1 scores a point in the product of the two numbers is even.
- Player 2 scores a point in the product of the two numbers is odd.
• A game consists of 10 turns.
Is their game fair? Explain why or why not.

​It's believed that as many as 22​% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. What sample size would allow us to increase our confidence level to​ 95% while reducing the margin of error to only 5​%?

There are A, B, and C types of problem set, and each type of problem set contains 3000, 2000, 5000
problems, respectively. Suppose you can solve A-type problem with 90% probability, B-type problem with
20% probability, and C-type problem with 60% probability. To pass graduation exam, you must solve both
of two questions randomly chosen from the total problem set (out of 10,000 problems). Answer the
following questions: