The probability of the random variable having a value between 4.1 and 7.4 can be calculated by finding the area under the curve between those two values.
First, calculate the base of the rectangle formed by the two values:
Base = 7.4 - 4.1 = 3.3
Next, calculate the height of the rectangle which is equal to the density of the curve, which is uniform:
Height = 1
Now, calculate the area of the rectangle:
Area = Base * Height
Area = 3.3 * 1
Area = 3.3
Finally, find the total area under the curve (total probability), which for a uniform distribution is 1. Divide the area of the rectangle by the total area to get the probability:
Probability = Area of rectangle / Total area
Probability = 3.3 / 10 (since the total area is 10)
Probability = 0.33
Therefore, the probability that the random variable has a value between 4.1 and 7.4 is 0.33, which is not one of the given answer choices. This may be due to the information provided being incomplete or incorrect.
Using the following uniform density curve, answer the question.
What is the probability that the random variable has a value between 4.1 and 7.4?
(1 point)
Responses
0.2875
0.5375
0.6625
0.4125
1 answer