The time, in minutes,  it takes a teacher to mark a set of assignments is uniformly distributed on the interval [38,90].  What is the probability that the next set of assignments will be marked in more than 59.06 minutes? Round the final answer to 2 decimal places

Given that the time it takes to mark a set of assignments is uniformly distributed on the interval \([38, 90]\), we can calculate the probability that the next set will take more than 59.06 minutes.

For a uniform distribution, the probability that a random variable \( X \) falls within a certain interval \([a, b]\) is given by:

\[
P(X > x) = \frac{b - x}{b - a}
\]

where \(a = 38\), \(b = 90\), and \(x = 59.06\).

### Calculation:

\[
P(X > 59.06) = \frac{90 - 59.06}{90 - 38} = \frac{30.94}{52} \approx 0.595
\]

Rounded to two decimal places:

\[
P(X > 59.06) \approx 0.60
\]

### Final Answer:
The probability that the next set of assignments will be marked in more than 59.06 minutes is approximately **0.60**.

Would you like a detailed explanation of the steps? Here are some related questions:

1. How is the formula for uniform distribution derived?
2. What are some real-life examples of uniform distribution?
3. How does uniform distribution differ from normal distribution?
4. Can this method be applied to non-uniform distributions?
5. How does the interval length affect the probability?

**Tip:** Always visualize uniform distributions with a simple graph, where the area under the curve represents the probability.

Explore how to calculate the probability of a uniform distribution scenario. Given a uniform distribution interval [38, 90], determine the likelihood that the next set of assignments will take more than 59.06 minutes. Detailed step-by-step solution provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation