Final answer:
The number of hours after which both Tae'Quan and Zlatan will charge the same amount for car repairs found as 2 hours. So, the option a. 2 hours is correct
Step-by-step explanation:
In order to determine the point at which both Tae'Quan and Zlatan will charge the same amount for car repairs, we employ the concept of a uniform distribution.
Let's designate x as the number of hours Tae'Quan spends on car repairs, with a uniform distribution between 1.5 and 4 hours.
Calculating the probability that Tae'Quan exceeds 2 hours involves finding the area to the right of 2 hours on the distribution curve, resulting in a uniform probability of 1.
For the probability of Tae'Quan taking less than 3 hours, the area to the left of 3 hours is computed, yielding a uniform probability of 0.6.
Determining the 30th percentile involves identifying the value below which 30% of the data lies.
Using the formula value = lower bound + (percentile * range), the 30th percentile corresponds to 2 hours.
This analytical approach provides a systematic means of addressing the problem within the context of uniform distribution.
Hence, the option a. 2 hours is correct.
Complete Question:
After how many hours will both Tae'Quan and Zlatan charge the same amount for car repairs where Tae'Quan spends on car repairs with a uniform distribution between 1.5 and 4 hours.
a. 2 hours
b. 3 hours
c. 4 hours
d. 5 hours