Question

1. let x = the number of watches owned by a randomly selected high school student. a histogram of the probability distribution of x is shown.

histogram of probability distribution with x - axis number of watches owned and y - axis probability

a. describe the shape of the distribution.

(handwritten: skewed right)

b. what is the probability that the number of watches owned by a randomly selected student is two or fewer?

c. find and interpret ( p(x = 1) ).

Explanation:

Part a:

Step1: Identify distribution shape

The histogram has the tallest bar on the left, with bars decreasing in height as the number of watches increases, meaning the tail extends to the right. This is a right-skewed (positively skewed) distribution.

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Part b:

Step1: Sum relevant probabilities

From the histogram, $P(X=0)=0.40$, $P(X=1)=0.25$, $P(X=2)=0.25$. Calculate $P(X \leq 2) = P(X=0)+P(X=1)+P(X=2)$

$$\begin{align*} P(X \leq 2) &= 0.40 + 0.25 + 0.25 \\ &= 0.90 \end{align*}$$

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Part c:

Step1: Read $P(X=1)$ from histogram

From the histogram, the probability for $X=1$ is 0.25.

Step2: Interpret the probability

This value represents the likelihood that a randomly chosen high school student has exactly 1 watch, or a 25% chance.

Answer:

a. Skewed right (positively skewed)
b. 0.90
c. $P(X=1)=0.25$; Interpretation: There is a 25% probability that a randomly selected high school student owns exactly 1 watch.