The mass, in grams, of a certain species of birds is uniformly distributed on the interval **[32.84,108.01]**.  What is the expected mass of a bird from this species? Round final answer to 2 decimal places

To find the expected mass of a bird from this species, we use the formula for the expected value (mean) of a uniformly distributed random variable. For a uniform distribution on the interval \([a, b]\), the expected value \(E(X)\) is given by:

\[
E(X) = \frac{a + b}{2}
\]

Given the interval \([32.84, 108.01]\), we can plug in the values:

\[
E(X) = \frac{32.84 + 108.01}{2} = \frac{140.85}{2} = 70.425
\]

Rounding to two decimal places, the expected mass is:

\[
\text{Expected mass} = 70.43 \text{ grams}
\]

Would you like further details or explanations?

Here are 5 related questions to expand on this concept:

1. How is the variance of a uniformly distributed random variable calculated?
2. What does the expected value represent in a uniform distribution?
3. How would the expected value change if the interval were shifted?
4. Can the expected value ever be outside the interval \([a, b]\) in a uniform distribution?
5. What is the probability of a bird having a mass greater than 90 grams in this distribution?

**Tip:** In a uniform distribution, every outcome within the interval is equally likely, making the expected value the midpoint of the interval.

Explore how to calculate the expected mass of a bird from a uniform distribution with an interval [32.84, 108.01] grams. Understand the concept of expected value in probability and uniform distributions. Suitable for advanced high school students and beyond.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation