In Exercises 9–12, using a loose interpretation of the criteri...

Question

In Exercises 9–12, using a loose interpretation of the criteria for determining whether a frequency distribution is approximately a normal distribution, determine whether the given frequency distribution is approximately a normal distribution. Give a brief explanation.
Best Actors Refer to the frequency distribution from Exercise 6

Best Actors Refer to the frequency distribution from Exercise 6

Table showing the age distribution of Best Actors when they won an Oscar, with frequency counts for each age range.

Accepted Answer

All right. Hello everyone. So this question says, a university professor recorded the final exam scores of students in a statistics course. The frequency distribution of their scores is shown below. Using a loose interpretation of the criteria for determining whether a frequency distribution is approximately normal, determine whether the given distribution is approximately normal, and give a brief explanation. And here we have 4 different answer choices labeled A through D. All right, so first and foremost, what does it mean for a frequency distribution to be approximately normal? Well, recall that two things have to be true, right? The first thing is that the frequencies have to increase to a peak and then decrease symmetrically. Now, more generally, the curve itself should be symmetrical with the highest values towards the middle. Because of that, we would expect a normal distribution to be bell-shaped. Which means that the highest frequency is found in the middle with the frequencies decreasing steadily on both sides of the peak. So, let's analyze for a second the frequency data that we are given. In this case, the highest value of 30 is in fact somewhere in the middle. Or rather, towards the middle of the data set. And then when you compare the values that are approaching the frequency of 30. They are steadily increasing before decreasing once more. But notice the difference in. The sharpness of that decrease on either side of our peak at 30. On the left On the left side of the curve. That value increases from 22 to 30, whereas after you reach the peak, the decrease is a little bit sharper from 30 now to 18. So, here, the decline after the peak is going to be sharper on the right, which would suggest a slight skew. Right, it's not perfectly symmetrical, but there are no extreme outliers or gaps in the data set. So here, using a rough definition, our correct answer is going to be option C in the multiple choice. Because the distribution is approximately normal, but it is slightly skewed to the left because the left tail is longer than the right. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.