Math Problem Statement
Determine the desired probability. P(X \le 2.55)
Solution
The estimated probability 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:
- How does linear interpolation work in estimating values between known points?
- What is the significance of the cumulative distribution function (CDF)?
- How would you compute using the CDF?
- Can the interpolation method be used for other types of distributions?
- 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.
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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)