Provide an appropriate response. Consider the discrete probability distribution given when answering the following question. Find the probability that x equals 5. x 3 5 7 8 P(x) 0.07 ? 0.16 0.12 0.65 3.25 0.35 1.75
Provide an appropriate response. Consider the discrete probability distribution given when answering the following question. Find the probability that x equals 5. x 3 5 7 8 P(x) 0.07 ? 0.16 0.12 0.65 3.25 0.35 1.75
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![**Question:**
Provide an appropriate response.
Consider the discrete probability distribution given when answering the following question. Find the probability that x equals 5.
\[
\begin{array}{c|cccc}
x & 3 & 5 & 7 & 8 \\
\hline
P(x) & 0.07 & ? & 0.16 & 0.12 \\
\end{array}
\]
- ❍ 0.65
- ❍ 3.25
- ❍ 0.35
- ❍ 1.75
**Explanation:**
The given table provides the probability distribution for a discrete random variable \(x\). To answer the question "Find the probability that \(x\) equals 5," we need to determine the unknown probability associated with \(x = 5\).
According to the principles of probability, the sum of the probabilities for all possible values of a discrete random variable should equal 1.
\[
P(x=3) + P(x=5) + P(x=7) + P(x=8) = 1
\]
Given:
\[
P(x=3) = 0.07, \quad P(x=7) = 0.16, \quad P(x=8) = 0.12
\]
So, we can write:
\[
0.07 + P(x=5) + 0.16 + 0.12 = 1
\]
Combining the known probabilities:
\[
0.35 + P(x=5) = 1
\]
Solving for \(P(x=5)\):
\[
P(x=5) = 1 - 0.35 = 0.65
\]
Therefore, the probability that \(x\) equals 5 is \(0.65\).
So the correct answer is:
- ❍ **0.65**
The other options are incorrect as they do not satisfy the condition that the sum of probabilities equals 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F68f51e6c-f342-4689-afb0-0310aec96525%2F6b7288f4-88aa-493a-9b86-48953e1d8dbf%2Fe2eqcce_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
Provide an appropriate response.
Consider the discrete probability distribution given when answering the following question. Find the probability that x equals 5.
\[
\begin{array}{c|cccc}
x & 3 & 5 & 7 & 8 \\
\hline
P(x) & 0.07 & ? & 0.16 & 0.12 \\
\end{array}
\]
- ❍ 0.65
- ❍ 3.25
- ❍ 0.35
- ❍ 1.75
**Explanation:**
The given table provides the probability distribution for a discrete random variable \(x\). To answer the question "Find the probability that \(x\) equals 5," we need to determine the unknown probability associated with \(x = 5\).
According to the principles of probability, the sum of the probabilities for all possible values of a discrete random variable should equal 1.
\[
P(x=3) + P(x=5) + P(x=7) + P(x=8) = 1
\]
Given:
\[
P(x=3) = 0.07, \quad P(x=7) = 0.16, \quad P(x=8) = 0.12
\]
So, we can write:
\[
0.07 + P(x=5) + 0.16 + 0.12 = 1
\]
Combining the known probabilities:
\[
0.35 + P(x=5) = 1
\]
Solving for \(P(x=5)\):
\[
P(x=5) = 1 - 0.35 = 0.65
\]
Therefore, the probability that \(x\) equals 5 is \(0.65\).
So the correct answer is:
- ❍ **0.65**
The other options are incorrect as they do not satisfy the condition that the sum of probabilities equals 1.
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