properties of probability distributions

A project is graded on a scale of 1 to 5. If the random variable, X, is the project grade, what is the mean of the probability distribution below?

1

A project is graded on a scale of 1 to 5. If the random variable, X, is the project grade, what is the mean of the probability distribution below? biggest one 3

3

A teacher assigns a score from 1 to 4 to each student project. The table below shows the probability distribution of the scores for a randomly selected student. Which score is most likely?

3

The number of siblings each student at a softball game has is recorded. The graph below shows the probability distribution of having any number of siblings, X, for a randomly selected student. Which number of siblings is least likely?

4 siblings

Which of the following describes the probability distribution below?

The median is greater than the mean, and the majority of the data points are to the right of the mean.

A family has two children. If B represents a boy and G represents a girl, the set of outcomes for the possible genders of the children is S = {BB, BG, GB, GG}, with the oldest child listed first in each pair. Let X represent the number of times G occurs. Which of the following is the probability distribution, PX(x)?

a

A school conducts a recipe contest in which 1 student gets first place, 1 student gets second place, 1 student gets third place, and 10 students tie for fourth place. Fifty students enter the contest. If X represents the distribution of prizes, which graph represents the probability distribution for a randomly selected student?

a

A spinner has two equal sections, one green and one orange. The spinner is spun three times, resulting in the sample space S = {GGG, GGO, GOG, OGG, GOO, OGO, OOG, OOO}. If the random variable X represents the number of times orange, O, is spun, which graph represents the probability distribution?

b

Which of the following represents a valid probability distribution?

b

A teacher asks her students to write down the number of hours studied, rounded to the nearest half hour. She compiles the results and develops the probability distribution below for a randomly selected student. What is the mean of the probability distribution?

d 1.50

The graph below shows the experimental probability of a runner finishing in first place (1), in second place (2), in third place (3), or not placing (4). Which of the following describes the probability distribution?

negatively skewed

A spinner is divided into five sections numbered 1 through 5. Juana records the number the spinner lands on for each of 50 spins. She computes and graphs the relative frequencies for each number. Which of the following describes the probability distribution?

positively skewed

Two fair dice, one yellow and one blue, are rolled. The value of the blue die is subtracted from the value of the yellow die. Which of the following best describes the theoretical probability distribution?

symmetric