Math Problem Statement

Consider the following data:

x −5 −4 −3 −2 −1 P(X=x) 0.2 0.3 0.2 0.1 0.2

Step 4 of 5 : Find the value of P(X≥−2) . Round your answer to one decimal place.

Solution

To find P(X2)P(X \geq -2), we sum the probabilities of all values of XX that are greater than or equal to 2-2.

From the given data:

P(X=2)=0.1P(X = -2) = 0.1 P(X=1)=0.2P(X = -1) = 0.2

Now, summing these probabilities:

P(X2)=P(X=2)+P(X=1)P(X \geq -2) = P(X = -2) + P(X = -1)

=0.1+0.2=0.3= 0.1 + 0.2 = 0.3

Rounding to one decimal place (though it's already in that form):

0.3\mathbf{0.3}

Would you like a breakdown of probability concepts?

Related Questions:

  1. What is the probability of P(X3)P(X \leq -3)?
  2. How do we verify that this is a valid probability distribution?
  3. What is the expected value E(X)E(X) of this distribution?
  4. How would the probability change if another value was added to the dataset?
  5. What is the variance of XX in this distribution?

Tip: Always check that the sum of all probabilities equals 1 to confirm a valid probability distribution!

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Math Problem Analysis

Mathematical Concepts

Probability
Discrete Probability Distribution
Summing Probabilities

Formulas

P(X ≥ -2) = P(X = -2) + P(X = -1)

Theorems

Probability Axioms
Valid Probability Distribution

Suitable Grade Level

Grades 8-10