Introduction to Random Variables

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?

12 and .972

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?

2 and .375

Let the random variable X = the number shown on a roll of an unfair die. The probability distribution is shown in the histogram. Identify the shape of the probability distribution histogram. approximately Normal skewed left symmetric approximately uniform

symmetric

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?

histogram a

Let the random variable X = the number shown on a roll of an unfair die. Identify the correct probability distribution histogram.

second graph where 2 to 5 is really low

Let the random variable X = the number of days a randomly selected respondent reported eating a cruciferous vegetable. The probability distribution is shown in the histogram. Identify the shape of the probability distribution histogram: approximately Normal skewed right skewed left approximately uniform

skewed right

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?

1 and .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).

3 or 4 and .754

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?

6 and .723