Question

show all your work. indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. the following frequency table summarizes the total amounts, in dollars, for 91 orders from a food truck during a certain day. amount frequency $0 up to but not including $5 8 $5 up to but not including $10 14 $10 up to but not including $15 25 $15 up to but not including $20 27 $20 up to but not including $25 12 $25 up to but not including $30 5 (a - i) use the data in the table to create a histogram showing the distribution of the amounts of the orders. (a - ii) describe the shape of the distribution of amounts.

Explanation:

Step1: Histogram creation

To create a histogram, we use the amount intervals on the x - axis and the frequencies on the y - axis. Each bar has a width equal to the class - interval width (in this case, 5) and a height equal to the frequency of the corresponding class.

Step2: Shape description

We sum up the frequencies: \(8 + 14+25 + 27+12 + 5=91\). To describe the shape, we look at the frequencies of the intervals. The frequencies increase from the first interval (\(0 - 5\)) to the fourth interval (\(15 - 20\)) and then start to decrease. This indicates a roughly bell - shaped or symmetric distribution.

Answer:

(a - i) A histogram with x - axis labeled as "Amount" with intervals \(0 - 5\), \(5 - 10\), \(10 - 15\), \(15 - 20\), \(20 - 25\), \(25 - 30\) and y - axis labeled as "Frequency" with bars of heights 8, 14, 25, 27, 12, 5 respectively.
(a - ii) The distribution is roughly bell - shaped or symmetric.