In Exercises 9–18, construct the histograms and answer the giv...

Question

In Exercises 9–18, construct the histograms and answer the given questions.

Burger King Dinner Service Times Use the frequency distribution from Exercise 18 in Section 2-1 to construct a histogram. Using a strict interpretation of the criteria for being a normal distribution, does the histogram appear to depict data from a population with a normal distribution?

Accepted Answer

All right, hello, everyone. So this question says, a researcher recorded the drive-through service times in seconds at a local fast food restaurant during dinner hours. Construct a histogram for yourself using the provided frequency distribution and answer the following question. Using a strict interpretation of the criteria for normality, does the histogram suggest the data follows a normal distribution. And here is the frequency distribution mentioned. So Here In order to construct the histogram, you have to begin with the midpoints of each class interval. And the midpoint, if you recall, is calculated by adding together. The lower bound and upper bound of a given class, and dividing that total by 2. So for each class, the midpoints are as follows. For the first, that's 37. For the second, it's 52. For the 3rd 67. For the 4th 82. For the 5th '97. For the 6th 112 and for the 7th interval 127. So the reason why the midpoints of each interval are necessary is because these are the values that are going to be on the X axis of the histogram. So starting off with a generic XY plot for a moment, as mentioned before, the midpoints of each interval are going to be found on the X axis. Whereas the Y axis is going to represent the frequency of each class. So here, the bars themselves are going to be drawn above each midpoint with the heights corresponding to the frequency values. So when you consider the first class, for example, with a midpoint of 37 and a frequency of 3, That bar in the histogram would be above 37. And as tall as 3 In the Y axis. So when all is said and done, This is what the histogram should look like. Now, you could construct the histogram using Microsoft Excel or on graph paper, but the result should look the same. And it should tell you the same information. So now analyzing the histogram for a second. First of all, we can see that the highest peak is in the middle of the graph. So it's towards the center. Not only is the highest point in the middle of the data set, we can see that on either side of this maximum, the data is steadily decreasing. But does this equal a normal distribution when considering a strict definition? A strict definition, if you recall, means that the normal distribution curve should be bell shaped. Which means that there has to be an element of symmetry with that peak in the middle, as mentioned before. Now in this particular case, it's worth mentioning that even though the highest point is in the center of the graph, The two tails on each end are not perfectly symmetric. Because the left tail has frequencies of 37, and 10 respectively. Whereas the right tail has frequencies of 85, and 2. Because these numbers are not equal, they're not perfectly balanced. This histogram is not exactly symmetrical, which means that it is not strictly normal, or the distribution is not strictly normal. So therefore Your answer is as follows. The histogram as mentioned is shown. And then the answer is no, the data is not. Strictly Normally distributed. And there you have it. And so with that being said, thank you so very much for watching, and I hope you found this helpful.

Key Concepts

Histogram

Normal Distribution

Criteria for Normality

Watch next