A State-Wide Math Test Consists of 50 True/False Questions and 40

question 54

Essay

A state-wide math test consists of 50 True/False questions and 40 multiple choice
questions with 5 answer options. The total score (TS) is equal to the number of
true/false items correct plus twice the number of multiple-choice items correct.
a) For students who are randomly guessing, the distribution of scores on the 50
True/False questions is a binomial distribution with probability of success equal to 0.50. If we define the random variable T = score from T/F items, what are the mean
and standard deviation of T for students who are guessing?
b) For students who are randomly guessing, the distribution of scores on the 40 multiple
choice questions is a binomial distribution with probability of success equal to 0.20.
If we define the random variable M = score from multiple choice items, what are the
mean and standard deviation of M for students who are guessing?
c) The total score, TS, is a random variable formed by calculating $$T + 2 M$$ Using your
results from parts (a) and (b), find the mean and standard deviation of the random
variable TS.
d) For students who randomly guess on the multiple choice part of the test, what is the
probability that the first question correct is the 4th question?

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Definitions:

Punitive Policies

Strategies or laws that are intended to punish individuals or entities for misconduct or crimes.

Truth in Sentencing

A legal principle that requires convicted individuals to serve a substantial portion of their sentence as imposed by the court, with limited possibilities for early release.

Longer Sentences

Refers to the imposition of extended periods of imprisonment as punishment for crimes.

Penal Sanctions

Penalties imposed for violating laws or regulations, which can include fines, imprisonment, or other forms of punishment.