2026-08-29T20:03:30.332553 image/svg+xml Matplotlib v3.10.9, https://matplotlib.org/ © EAGLE BEACON GLOBAL 012340251020Waiting time (minutes)Frequency densi...
Question 1 Report
A bakery surveys how long, in minutes, customers wait in the queue during its Saturday morning rush. The histogram shows the frequency density for each waiting-time interval.
- Work out the number of customers who waited between 2 and 5 minutes. (1)
- Work out the number of customers who waited between 5 and 10 minutes. (1)
- Work out the number of customers who waited between 10 and 20 minutes. (1)
- Work out the total number of customers surveyed. (1)
- Work out the percentage of customers who waited 10 minutes or more, giving your answer to 3 significant figures. (1)
Answer Details
On a histogram, frequency is frequency density multiplied by class width; adding every class's frequency gives the total surveyed, and a "10 minutes or more" percentage is found by summing the frequencies of every class at or beyond that boundary, dividing by the total, and converting to a percentage.
- The histogram shows a frequency density of \(4\) for the \(2\) to \(5\) minute class (width \(3\)): \(4\times3=12\) customers [1 mark]
- The frequency density for the \(5\) to \(10\) minute class (width \(5\)) is \(1.6\): \(1.6\times5=8\) customers [1 mark]
- The frequency density for the \(10\) to \(20\) minute class (width \(10\)) is \(0.5\): \(0.5\times10=5\) customers [1 mark]
- Total \(=6+12+8+5=31\) customers, where \(6\) is the frequency of the remaining (\(0\) to \(2\) minute) class read from the histogram. [1 mark]
- Customers waiting \(10\) minutes or more \(=5\); as a percentage of the total, \(5\div31\times100=16.1\%\) (3 s.f.). [1 mark]
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