a) Find P(at least 7)= b)Find P(at most 5)=ENTER YOUR ANSWER TO 2 DECIMAL PLACES The table shown represents a probability distribution with calculations of expected values. It includes the following columns:1. **X**: A random variable taking values 3, 4, 5, 6, 7, and 8.2. **P(X)**: The probability associated with each value of X. - P(3) = 0.18 - P(4) = 0.2 - P(5) = 0.17 - P(6) = 0.42 - P(7) = 0.02 - P(8) = 0.013. **X P(X)**: The product of the random variable X and its probability P(X), which represents the contribution of each value to the expected value of X. - 3 * 0.18 = 0.54 - 4 * 0.2 = 0.80 - 5 * 0.17 = 0.85 - 6 * 0.42 = 2.52 - 7 * 0.02 = 0.14 - 8 * 0.01 = 0.08 The sum of these values, Σ X P(X), is 4.93.4. **X² P(X)**: The product of the square of the random variable X and its probability P(X), which is used in variance calculations. - 3² * 0.18 = 1.62 - 4² * 0.2 = 3.20 - 5² * 0.17 = 4.25 - 6² * 0.42 = 15.12 - 7² * 0.02 = 0.98 - 8² * 0.01 = 0.64 The sum of these values, Σ X² P(X), is 25.81.The table includes totals at the bottom: - The total probability Σ P(X) is 1, confirming the probabilities are correctly normalized.- Σ X P(X) = 4.93, the expected value of X.- Σ X² P(X) = 25.81, useful for calculating variance and standard deviation.

Given probability distribution table: X P(X) 3 0.18 4 0.2 5 0.17 6 0.42 7 0.02 8 0.01

Answered: a) Find P(at least 7)= b)Find P(at…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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a) Find P(at least 7)=

b)Find P(at most 5)=

ENTER YOUR ANSWER TO 2 DECIMAL PLACES

The table shown represents a probability distribution with calculations of expected values. It includes the following columns:

1. **X**: A random variable taking values 3, 4, 5, 6, 7, and 8.

2. **P(X)**: The probability associated with each value of X.
- P(3) = 0.18
- P(4) = 0.2
- P(5) = 0.17
- P(6) = 0.42
- P(7) = 0.02
- P(8) = 0.01

3. **X P(X)**: The product of the random variable X and its probability P(X), which represents the contribution of each value to the expected value of X.
- 3 * 0.18 = 0.54
- 4 * 0.2 = 0.80
- 5 * 0.17 = 0.85
- 6 * 0.42 = 2.52
- 7 * 0.02 = 0.14
- 8 * 0.01 = 0.08

The sum of these values, Σ X P(X), is 4.93.

4. **X² P(X)**: The product of the square of the random variable X and its probability P(X), which is used in variance calculations.
- 3² * 0.18 = 1.62
- 4² * 0.2 = 3.20
- 5² * 0.17 = 4.25
- 6² * 0.42 = 15.12
- 7² * 0.02 = 0.98
- 8² * 0.01 = 0.64

The sum of these values, Σ X² P(X), is 25.81.

The table includes totals at the bottom:
- The total probability Σ P(X) is 1, confirming the probabilities are correctly normalized.
- Σ X P(X) = 4.93, the expected value of X.
- Σ X² P(X) = 25.81, useful for calculating variance and standard deviation.

Expert Solution

Step 1

$\mathbf{Solution}$

Given probability distribution table:

X	P(X)
3	0.18
4	0.2
5	0.17
6	0.42
7	0.02
8	0.01

$\mathrm{{\color{Blue} \mathbf{a)} }\;\mathbf{Find}:\; P(at \;least\; 7)=?}$

$\mathrm{P(at \;least\; 7)=P(7)+P(8)}$

$\mathrm{P(at \;least\; 7)=0.02+0.01}$

$\mathrm{P(at \;least\; 7)=\mathbf{{\color{Red} 0.03}}}$

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a) Find P(at least 7)= b)Find P(at most 5)= ENTER YOUR ANSWER TO 2 DECIMAL PLACES