In Exercises 3 and 4, (a) construct a probability distribution...

Question

In Exercises 3 and 4, (a) construct a probability distribution, and (b) graph the probability distribution using a histogram and describe its shape.

The number of hours students in a college class slept the previous night

hist

Accepted Answer

All right, hello, everyone. So this question says, a survey was conducted to record the number of books read by students in a literature class during the last month. The data collected is as follows. Graph the histogram representing the probability distribution for the number of books read. Then describe the shape of the distribution. So here on the screen, I went ahead and made a table with all of the values of X given, which in this case represents the number of books read by students. Now, the column on the right represents the probability of each X value for the probability distribution. But recall that in order to find this, we first have to know the total number of students in the class. So in this case The total number of students is the sum of all the students in each category. So that's the sum of 2, 1415, 13, 52, and 1. And this is equal to 52. So to find the probability of each number of books read, you would divide the number of students in each category by the total number of students. So for zero books, for example, that would be 2 divided by 52. Which equals approximately 0.04. For one book that's 14 divided by 52. Which gives you 0.27. For two books, that's 15/52. Which gives you 0.29. For 3 books, that's 13/52, which gives you 0.25. 44 books, yeah, if you scroll down. That is 5/52. Which gives you 0.10. For 5 books, that's 2 divided by 52 or 0.04. And then for 6 books, that's 1 divided by 52, or approximately 0.02. So, here, recall that all probabilities should have a sum of 1 or 100%. When you add the probability values obtained just now, that comes out to 1.01. And it's not exactly one, but it is very close to one. Recall that this tends to happen because of the rounding done on each probability. So that's acceptable. Once again, though, as long as it remains very close to one. So it's at this point that you would now construct the histogram. Recall that the X axis is going to indicate the number of books read ranging from 0 to 6, and then the Y axis is going to showcase the probability for each number. So, because the highest probability in our distribution is 0.29, we can set 0.30 as the maximum number. For the histogram itself. And so dividing our maximum, that's 0.30 by, let's say 6, gives you a spacing along the vertical of 0.05. So So here on the screen, I have what the histogram should look like. And now let's talk about the shape. So looking at the shape of the histogram, you can see that it's not symmetric. Meaning that the highest probability is not in the center of the data set or the distribution. Now, specifically, you can see that the highest values of the data set are actually skewed towards the left. With the peak being at 2 books. And after the peak at 2 books, the data itself begins to gradually decrease towards higher numbers. Now, because the data is clustered towards The left side, the tail of the distribution is longer on the right than it is on the left. And so because of the fact that the tail is longer on the right, this is a right skewed distribution. So, we would say that this histogram is skewed right. Which tells you that more students tend to read less books while fewer students read several books. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

In Exercises 3 and 4, (a) construct a probability distribution, and (b) graph the probability distribution using a histogram and describe its shape.

The number of hours students in a college class slept the previous night

Key Concepts

Probability Distribution

Histogram

Shape of Distribution

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