Question

1. the graph displays the cumulative relative frequency of the lengths of phone calls made from the math department office at gabalot high school last month. a. about what percent of calls lasted 30 minutes? b. estimate and interpret the first quartile of the distribution.

Explanation:

Step1: Recall the concept of cumulative relative - frequency

The cumulative relative - frequency at a value \(x\) gives the proportion of data values that are less than or equal to \(x\).

Step2: Answer part (a)

To find the percent of calls that lasted 30 minutes, we note that the cumulative relative - frequency at 30 minutes is approximately 67%. To find the percent of calls that lasted exactly 30 minutes, we need to find the difference in cumulative relative - frequencies. Let \(F(x)\) be the cumulative relative - frequency function. The cumulative relative - frequency at 25 minutes is approximately 40%. So the percent of calls that lasted 30 minutes is \(67 - 40=27\%\).

Step3: Recall the definition of the first - quartile

The first quartile \(Q_1\) is the value such that 25% of the data lies below it.

Step4: Estimate the first quartile from the graph

Looking at the cumulative relative - frequency graph, we find the value of \(x\) for which the cumulative relative - frequency is 25%. From the graph, the first quartile is approximately 12 minutes. This means that about 25% of the phone calls made from the math department office lasted 12 minutes or less.

Answer:

a. About 27%
b. The first quartile is approximately 12 minutes. This means that about 25% of the phone calls made from the math department office lasted 12 minutes or less.