Question

an individual stock is selected at random from the portfolio represented by the box - and - whisker plot shown to the right. find the probability that the stock price is (a) less than $22, (b) between $22 and $57, and (c) $34 or more.
(a) the probability that the stock price is less than $22 is 0.25. (do not round.)
(b) the probability that the stock price is between $22 and $57 is □. (do not round.)

Explanation:

Step1: Recall the properties of box - and - whisker plot and probability formula

In a box - and - whisker plot, the data is divided into four equal parts (quartiles). The probability of an event \(P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Since the box - and - whisker plot divides the data into four equal parts (each part represents \(25\%\) or \(0.25\) of the data).

Step2: Calculate the probability for part (b)

The value \(22\) is the first quartile (\(Q_1\)) and \(57\) is the third quartile (\(Q_3\)). The data between \(Q_1\) and \(Q_3\) represents two - quartiles.
Since each quartile represents \(0.25\) of the data, the probability \(P(22\lt x\lt57)\) is \(0.25 + 0.25\)

Answer:

\(0.5\)