[APPLET] Milk Consumption You are performing a study about wee...

Question

[APPLET] Milk Consumption You are performing a study about weekly per capita milk consumption. A previous study found weekly per capita milk consumption to be normally distributed, with a mean of 48.7 fluid ounces and a standard deviation of 8.6 fluid ounces. You randomly sample 30 people and record the weekly milk consumptions shown below.

a. Draw a frequency histogram to display these data. Use seven classes. Do the consumptions appear to be normally distributed? Explain.

Data table displaying weekly milk consumption values for a sample of 30 individuals, ranging from 25 to 65 fluid ounces.

a. Draw a frequency histogram to display these data. Use seven classes. Do the consumptions appear to be normally distributed? Explain.

Accepted Answer

All right, hello, everyone. So this question says, a researcher is analyzing the daily caffeine intake of 30 college students. A previous survey found that daily coffee intake is normally distributed with a mean of 12.5 fluid ounces, and a standard deviation of 3.2 fluid ounces. Draw a frequency histogram to display this data. Use 7 classes. Do the consumptions appear to be normally distributed? And here we have the data for all 30 students. So, before anything else, right, step one is to organize the data. Specifically, you are to Rewrite the data set in order from the smallest to the largest value. And here, I actually went ahead and did that in advance, just in the interest of time. So let me go ahead and reveal that. So now, with the data set in order, we can find the range and the class width. So, here we can see our minimum. Is 8 And our maximum is 19. So the range is equal to 19 subtracted by 8, which equals 11. So now, the class width or CW as I'm writing here for short, is equal to the range of the data set, divided by the number of classes that you want. So here that's 11 divided by 7. Which equals approximately 1.57. But In this context, we're going to round this up to 2. So the class width for this histogram is going to be 2. And now We can create our class intervals. And so with the class intervals. We can begin with our frequency distribution. All right, so here you can see that the class intervals are as follows, from 8 to 9, 10 to 1112 to 1314 to 1516 to 1718 to 19, and 20 to 21. And here on the right, you can see the frequency, which represents the number of data of data values, excuse me, that fall into each class interval. So after going through the data set. And finding the frequency of each class interval, the frequencies in the order of each class interval is as follows. We have 2 4 12 8. 31 and 0. So now It is this information on the table. That you would use to draw the histogram. So the X axis represents each class interval and the Y axis. Corresponds to the frequency of each class interval. And so when you draw out the histogram. This is what the histogram itself should look like. So now, let's talk about the sheep. Here you can see that the distribution is going to peak around the center, that is between 12 and 13 fluid ounces. Now, this is in accordance with the expected mean of 12.5 fluid ounces. And because the peak is around the center, this does show a bell-shaped curve. Now, it's not perfectly symmetrical, because notice how the class interval 10 to 11 does not have the same frequency as the class interval 14 to 15. But, We can say that the distribution is approximately normal because it does peak around the middle. And that if you recall, is a feature of a normal distribution. So now this leads you to the final answer. As mentioned before, here we have the histogram. And the distribution appears to be approximately normal, though not perfectly symmetric. And there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.

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Key Concepts

Normal Distribution

Histogram

Sampling Distribution

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