Introduction to Random Variables

Question 1

A fair coin will be tossed 3 times. Let the random variable X = the number of tails among the 3 tosses. The probability distribution of X is given in the table. What is the probability that the coin lands on tails twice? P(X = ) =

Revolt · Accepted Answer

Selection 1: 2; Selection 2: 0.375

Question 2

A fair coin will be tossed 3 times. Let the random variable X = the number of tails among the 3 tosses. The probability distribution of X is given in the table. What is the probability that the coin lands on tails more than once? P(X > ) =

Revolt · Accepted Answer

Selection 1: 1; Selection 2: 0.5

Question 3

A pair of fair dice will be rolled. Let the random variable X = the sum of the numbers shown on their faces. The probability distribution of X is given in the table. What is the probability that the dice show a sum of at least 6? P(X ≥ ) =

Revolt · Accepted Answer

6; Selection 1: 6; Selection 2: 0.723

Question 4

A pair of fair dice will be rolled. Let the random variable X = the sum of the numbers shown on their faces. The probability distribution of X is given in the table. What is the probability that the dice do not show a sum of 12? P(X ≠ ) =

Revolt · Accepted Answer

12; Selection 1: 12; Selection 2: 0.972

Question 5

The final letter grades earned by students in a large psychology class were converted to grade points in order to calculate the students’ GPAs. An A = 4 points, a B = 3 points, etc. Let the random variable X = the grade point earned by a randomly selected student. The probability distribution of X is given in the table. Find and interpret P(X ≥ 3). The probability that a randomly selected student earned a grade point of is .

Revolt · Accepted Answer

3 or 4; Selection 1: 3 or 4; Selection 2: 0.754

Question 6

A farming council takes a large random survey of US adults in which they ask how many times they ate a cruciferous vegetable such as broccoli, cauliflower, or cabbage in the last 7 days.Let the random variable X be the number of days a randomly selected respondent reported eating one of these vegetables.The probability distribution of X and several choices of histograms are shown here.Which histogram correctly displays the probability distribution of the random variable X, the number of days a randomly selected respondent reported eating a cruciferous vegetable?

Revolt · Accepted Answer

histogram A

Question 7

Identify the shape of the probability distribution histogram.

Revolt · Accepted Answer

symmetric

Question 8

Question 11

Revolt · Accepted Answer

0.723

Question 9

Question 12

Revolt · Accepted Answer

0.972

Question 10

Question 13

Revolt · Accepted Answer

0.754

Introduction to Random Variables Answers

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