Question

ann is a dedicated skee ball player who always rolls for the 50 - point slot.
the probability distribution of ann’s score x on a randomly selected roll of
the ball is shown here.

score	10	20	30	40	50

(a) is x a discrete or a continuous random variable?
explain your answer.

• x is a continuous random variable because it can

take any value in an interval on the number line.

• x is a discrete random variable because it can

take any value in an interval on the number line.

• x is a discrete random variable because it takes

a fixed set of numerical values with gaps
between them.

• x is a continuous random variable because it

takes a fixed set of numerical values with gaps
between them.
(b) find ( p(x > 20) ). explain in words what this
probability means.

• ( p(x > 20) = 0.68 ). this is the probability that

ann scores 20 points or more on a randomly
selected roll.

• ( p(x > 20) = 0.41 ). this is the probability that

ann scores more than 20 points on a randomly
selected roll.

• ( p(x > 20) = 0.68 ). this is the probability that

ann scores more than 20 points on a randomly
selected roll.

• ( p(x > 20) = 0.41 ). this is the probability that

ann scores 20 points or more on a randomly
selected roll.
(c) find the probability that anna scores at most 20 on a randomly selected roll.
(round to 2 decimal places.)

Explanation:

Part (a)

Step1: Recall definitions

Discrete random variables take a fixed set of numerical values (like 10, 20, 30... here) with gaps between them. Continuous variables take any value in an interval.

Step2: Analyze X

Anna’s score \( X \) can only be 10, 20, 30, 40, 50 (fixed set with gaps), so it’s discrete. The correct option is: "X is a discrete random variable because it takes a fixed set of numerical values with gaps between them."

Step1: Define \( P(X > 20) \)

\( P(X > 20) \) means the probability that \( X \) is 30, 40, or 50 (since \( X > 20 \) excludes 10 and 20).

Step2: Calculate probabilities

From the table, \( P(30) = 0.19 \), \( P(40) = 0.15 \), \( P(50) = 0.07 \). Sum them: \( 0.19 + 0.15 + 0.07 = 0.41 \). This represents the probability that Anna scores more than 20 points on a randomly selected roll. The correct option is: " \( P(X > 20) = 0.41 \). This is the probability that Anna scores more than 20 points on a randomly selected roll."

Step1: Define "at most 20"

"At most 20" means \( X \leq 20 \), so \( X = 10 \) or \( X = 20 \).

Step2: Calculate probabilities

From the table, \( P(10) = 0.32 \), \( P(20) = 0.27 \). Sum them: \( 0.32 + 0.27 = 0.59 \).

Answer:

X is a discrete random variable because it takes a fixed set of numerical values with gaps between them. (The corresponding option: the third option in part (a))

Part (b)