A density graph for all of the possible times from 50 seconds to 200 seconds can be used to find which of the following?
A. The probability of a time from 75 seconds to 250 seconds
B. The probability of a time from 75 seconds to 150 seconds
C. The probability of a time from 25 seconds to 150 seconds
D. The probability of a time from 150
seconds to 250 seconds
A density graph for all of the possible times from 50 seconds to 200 seconds can be used to find which of the following?
A density graph represents the distribution of data over a range of values, usually displayed in the form of a curve. To use the density graph to find the probability of a specific range of times, you need to look at the area under the curve within that range.
In this case, the density graph represents all possible times from 50 seconds to 200 seconds. To find the probability of a time within a specific range, you need to look at the area under the curve within that range.
Option A: The probability of a time from 75 seconds to 250 seconds. The range mentioned in this option goes beyond the range covered by the density graph (50 seconds to 200 seconds). Therefore, the density graph cannot be used to find the probability of a time in this range.
Option B: The probability of a time from 75 seconds to 150 seconds. This range falls within the range covered by the density graph (50 seconds to 200 seconds). Therefore, the density graph can be used to find the probability of a time in this range.
Option C: The probability of a time from 25 seconds to 150 seconds. This range includes the starting point (25 seconds) of the density graph. However, the ending point (150 seconds) falls outside the range covered by the density graph (50 seconds to 200 seconds). Therefore, the density graph cannot be used to find the probability of a time in this range.
Option D: The probability of a time from 150 seconds to 250 seconds. The starting point of this range (150 seconds) falls within the range covered by the density graph (50 seconds to 200 seconds). However, the density graph does not cover the ending point (250 seconds) of this range. Therefore, the density graph cannot be used to find the probability of a time in this range.
Based on the above analysis, option B, the probability of a time from 75 seconds to 150 seconds, can be found using the density graph.
To find the answer, we first need to understand what a density graph represents. A density graph, also called a probability density function (PDF), shows the relative frequency of values within a certain range. In this case, the graph represents the density of times from 50 seconds to 200 seconds.
To answer the question, we need to consider the range of times given and compare it to the range represented by the density graph.
Option A: The probability of a time from 75 seconds to 250 seconds.
This range extends beyond the range represented by the density graph, which only goes up to 200 seconds. Therefore, option A is incorrect.
Option B: The probability of a time from 75 seconds to 150 seconds.
This range falls within the range represented by the density graph, which goes up to 200 seconds. Therefore, option B is a possible answer.
Option C: The probability of a time from 25 seconds to 150 seconds.
This range extends below the range represented by the density graph. The density graph starts at 50 seconds, so it does not provide information about times before that. Therefore, option C is incorrect.
Option D: The probability of a time from 150 seconds to 250 seconds.
This range extends beyond the range represented by the density graph, which only goes up to 200 seconds. Therefore, option D is incorrect.
In conclusion, the correct answer is B. The density graph can be used to find the probability of a time from 75 seconds to 150 seconds.
If you have the two extreme limits to your graph as '50' and '200' seconds, then the interval that you can find information about cannot have a time value less than 50, or more than 200.
For example, it cannot be (A) because 250 seconds is more than 200.
Which option fits this criteria?