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 with x-axis: number of watches owned (0,1,2,3) 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? (handwritten: 0.90)

c. find and interpret p(x = 1). (handwritten: .30)
(handwritten: there is a 30% probability that a randomly selected student owns 1 watch.)

Explanation:

a. The histogram has the tallest bar on the left, with bars decreasing in height as the number of watches increases, which defines a right-skewed distribution.
b. Add the probabilities for $X=0$, $X=1$, and $X=2$: $0.40 + 0.30 + 0.20 = 0.90$.
c. The height of the bar for $X=1$ is 0.30, which represents the probability a randomly selected student owns exactly 1 watch.

Answer:

a. Right-skewed (positively skewed)
b. 0.90
c. $P(X=1)=0.30$; There is a 30% probability that a randomly selected high school student owns exactly 1 watch.