Final answer:
The 45th percentile (P45) of professor's classes that have a continuous uniform distribution between 49.29 min and 55.55 min is calculated using the formula for uniform distribution percentiles and is approximately 52.107 minutes.
Step-by-step explanation:
The question involves finding the 45th percentile (denoted as P45) of a continuous uniform distribution for the duration of a professor's classes. The classes are uniformly distributed between 49.29 minutes and 55.55 minutes.
Step-by-Step Solution:
- First, note that in a uniform distribution, the percentiles are spread evenly across the range. You can find any percentile by using the formula: P = a + (b - a)(n), where P is the percentile, a is the minimum value, b is the maximum value, and n is the desired percentile in decimal form.
- Turn the desired 45th percentile into decimal form by dividing by 100 (0.45).
- Substitute the known values into the formula: P = 49.29 + (55.55 - 49.29)(0.45) to find P45.
- Calculate the value to get P45: P = 49.29 + (6.26)(0.45) which gives us P = 49.29 + 2.817, so P45 ≈ 52.107 minutes.
Therefore, if one class is randomly selected, P45 is approximately 52.107 minutes.