Math Problem Statement

Determine the desired probability. P(X \le 2.55)

Determine the desired probability. P(X ≤ 2.55)

Solution

The estimated probability P(X2.55)P(X \leq 2.55) is approximately 0.8453 based on the given CDF values.

Would you like further details on this interpolation process or any additional clarifications?

Here are 5 related questions to explore further:

  1. How does linear interpolation work in estimating values between known points?
  2. What is the significance of the cumulative distribution function (CDF)?
  3. How would you compute P(X>2.55)P(X > 2.55) using the CDF?
  4. Can the interpolation method be used for other types of distributions?
  5. How would you compute probabilities for continuous distributions without a table?

Tip: CDF values are useful because they give the probability that a random variable will take a value less than or equal to a given number.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Probability
Cumulative Distribution Function (CDF)
Linear Interpolation

Formulas

CDF P(X ≤ x) gives the probability that the random variable X takes a value less than or equal to x
Linear interpolation formula: P(X ≤ x) ≈ P(X ≤ x_1) + [(x - x_1) / (x_2 - x_1)] * [P(X ≤ x_2) - P(X ≤ x_1)]

Theorems

Cumulative Distribution Function (CDF) Theorem

Suitable Grade Level

College/University Level (Statistics or Probability Course)