Math Problem Statement

Suppose a random variable X follows a uniform distribution with minimum 10 and maximum 50. What is the probability that X takes a value greater than 35? Please enter your answer rounded to 4 decimal places.

Solution

For a uniform distribution XX on the interval [a,b][a, b], the probability P(X>c)P(X > c) can be calculated using the formula:

P(X>c)=bcbaP(X > c) = \frac{b - c}{b - a}

In this case, a=10a = 10, b=50b = 50, and c=35c = 35. Plugging in the values:

P(X>35)=50355010=1540=38P(X > 35) = \frac{50 - 35}{50 - 10} = \frac{15}{40} = \frac{3}{8}

Now, converting 38\frac{3}{8} to a decimal:

P(X>35)=0.3750P(X > 35) = 0.3750

Thus, the probability that XX takes a value greater than 35 is 0.3750 (rounded to four decimal places).

If you have any questions or need further clarification, feel free to ask! Here are some related questions you might consider:

  1. How do you calculate the mean and variance of a uniform distribution?
  2. What happens to the probability if the range of the uniform distribution is changed?
  3. Can you explain how to calculate probabilities for continuous distributions?
  4. How would you find the probability that XX is less than 20?
  5. What are the properties of a uniform distribution?

Tip: When working with uniform distributions, remember that all intervals within the range have equal probabilities.

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Math Problem Analysis

Mathematical Concepts

Probability
Uniform Distribution

Formulas

P(X > c) = (b - c) / (b - a)

Theorems

Properties of Uniform Distribution

Suitable Grade Level

Grades 9-12