Determine Whether the Given Procedure Results in a Binomial Distribution

question 102

Essay

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
-Multiple-choice questions on a test each have 4 possible answers, one of which is correct. Assume that you
guess the answers to 4 such questions.
a. Use the multiplication rule to find the probability that the first two guesses are wrong and the third and
fourth guesses are correct. That is, find P(WWCC), where C denotes a correct answer and W denotes a wrong
answer.
b. Make a complete list of the different possible arrangements of 2 wrong answers and 2 correct answers, then
find the probability for each entry in the list.
c. Based on the preceding results, what is the probability of getting exactly 2 correct answers when 4 guesses are
made?

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Definitions:

Factorial ANOVA

A statistical analysis used to examine the effects of two or more categorical independent variables on one continuous dependent variable.

T-test

A statistical method employed to evaluate if there's a significant difference between the average values of two distinct groups.

Null Hypotheses

A statement positing that no statistical relation or significance exists in a set of given observations.

Factorial Analysis

Factorial analysis is another term for factor analysis, a technique employed in statistics to explore underlying factors or components that explain the variability among observed variables.