Answer:
1. The longest time waited in line was 13 minutes; 2. The number of customers that waited for 7.2 minutes is 138, approximately.
Step-by-step explanation:
The key to answering this question is to manage the concepts of <em>range</em> and <em>percentile</em> in a distribution of data. We can roughly say that range is the difference between the <em>highest</em> and the <em>lowest</em> values in the distribution (a measure of dispersion), and percentile tells us what percentage of the data is below it.
The question says nothing about the kind of distribution the data follow. However, with the given information, we can overcome the question.
<h3>1. What was the longest time (in minutes) anyone waited in line? </h3>
According to the description in the question "the range of the data was 13 minutes and the fastest anyone was checked out was 1.4 minutes".
This gives us a range of values from 1.4 minutes to 13 minutes for <em>time customers wait for being checked</em>, in which 1.4 minutes was <em>the fastest</em> in being checked and 13 minutes the <em>longest time</em> in being checked.
Therefore, the longest time waited in line was 13 minutes.
<h3>2. Approximately how many customers waited 7.2 minutes?</h3>
A <em>60th</em> percentile indicates that 60% of the observations are below it, a <em>50th</em> percentile indicates that 50% of the observations are lower than it, and so on. That is, a percentile is a way to say <em>the percentage of observations that are below it</em>.
From the question, we already know that 90th and 60th percentiles are <em>9.7 minutes</em> and <em>7.2 minutes</em>, respectively. In other words, the <em>90th percentile is 9.7 minutes</em> and the <em>60th percentile is 7.2 minutes</em>. For the latter, we can say that 60% of the customers were attended below 7.2 minutes. Then, knowing that the sample was of 230 customers, we can determine the number of customers that waited for less than 7.2 minutes (60th percentile) as follows:
Thus, according to the definition of percentile, the number of customers that waited for less than 7.2 minutes is 138. However, we cannot say anything for those that wait exactly 7.2 minutes, only those that waited lower than 7.2 minutes (for example, 7.19 minutes). In this way, we can say that the number of customer that waited 7.2 minutes is, <em>approximately</em>, 138.