In Exercises 35–38, the bar graph shows the results of a surve...

Question

In Exercises 35–38, the bar graph shows the results of a survey in which 8806 undergraduate students were asked how many hours they spend on studying and other academic activities outside of class in a typical week. (Source: American College Health Association)

37. Find the probability of randomly selecting an undergraduate who does not study from 6 to 10 hours per week.

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37. Find the probability of randomly selecting an undergraduate who does not study from 6 to 10 hours per week.

Accepted Answer

Welcome back everyone another video. A survey of 9500 college students asked how many hours per week they spend exercising. The results are shown below. What is the probability that a randomly selected student does not exercise between 6 and 8 hours per week? A 0.289. B 0.711. C 0.811 and D 0.189. So for this problem we're looking for probability and we're given a histogram. So first of all, whenever we want to identify the probability of an event A, let's suppose that an event A represents that a student does not exercise between 6 and 8 hours per week. We want two numbers, the number of favorable outcomes and. And the number of total outcomes m. So It's going to be the total number of students, right? Essentially, we're going to add all of the numbers given to us in the histogram for each interval of hours per week. So let's begin adding them. First of all, between 0 and 2, we have 1200. We're going to add 2100 for 3 to 5 hours and we're going to continue. So the next one is 1800, 1600. 900 And finally 1900. So when we add these numbers, we get 9500, and this is the total number of outcomes. Now, we want to identify the probability of an event that the student does not exercise between 6 and 8 hours per week. So to make it really simple, and instead of using the addition rule, we're going to use the method of compliments. Let's recall that. The probability of A is 1 minus the probability of the complement of A, right? So now, the probability of a bar or the complement of A is the probability of an event that a student exercises between 6 and 8 hours per week. So the number of favorable outcomes is 1800. And we are dividing by the total number of outcomes 9500. And what we're going to do is simply use this property to identify the probability of A. This is 1 minus 1800. Divided by 9500. Which is equal to 7700. Divided by 9500, and this is equal to 0.811. Which corresponds to the answer to a C. Thank you for watching.

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Key Concepts

Probability

Bar Graph Interpretation

Complementary Events

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