Fill in the missing value so that the following table represents a probability distribution.

 row chart ( (x   -5   -4    -3   -2  )(P(x)    0.06   0.51   ?   0.04) )

For a table to represent a valid probability distribution, the sum of all probabilities \( P(x) \) must equal 1.

Given the table:

\[
\begin{array}{|c|c|c|c|c|}
\hline
x & -5 & -4 & -3 & -2 \\
\hline
P(x) & 0.06 & 0.51 & ? & 0.04 \\
\hline
\end{array}
\]

We need to find the missing value \( P(-3) \).

The sum of the probabilities should satisfy:

\[
0.06 + 0.51 + P(-3) + 0.04 = 1
\]

Simplifying the known values:

\[
0.61 + P(-3) = 1
\]

Solving for \( P(-3) \):

\[
P(-3) = 1 - 0.61 = 0.39
\]

Thus, the missing value is \( P(-3) = 0.39 \).

Would you like any further details or clarifications?

Here are 5 related questions:
1. How do you check if a probability distribution is valid?
2. What are the properties of a probability distribution?
3. Can a probability value be negative?
4. What is the total probability of all possible outcomes in a distribution?
5. How can you calculate expected value from a probability distribution?

**Tip**: The sum of probabilities in any valid probability distribution must always equal 1.

Fill in the missing value so that the following table represents a probability distribution. Row chart: (x: -5, -4, -3, -2) (P(x): 0.06, 0.51, ?, 0.04)

Solve the probability distribution table by finding the missing value P(-3) such that the sum of probabilities equals 1. The given values are P(-5) = 0.06, P(-4) = 0.51, and P(-2) = 0.04. Learn how to use probability sum rules to solve this problem, ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation