56) The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. P(x) 0.14 2 0.16 3 0.12 4 0.14 5 0.13 0.31 A)μ= 0.2 B ) μ = 3.8 Ομ= 3.5 D ) μ = 39

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56) The accompanying table shows the probability distribution for x, the number that shows up when a loaded die
is rolled.

**Probability Distribution for a Loaded Die**

This example demonstrates a probability distribution for \( x \), where \( x \) is the number that appears when a loaded die is rolled. The distribution is detailed in the following table:

| \( x \) | \( P(x) \) |
|---------|------------|
| 1       | 0.14       |
| 2       | 0.16       |
| 3       | 0.12       |
| 4       | 0.14       |
| 5       | 0.13       |
| 6       | 0.31       |

**Options for the Mean (\( \mu \)) of the Distribution:**

A) \( \mu = 0.2 \)  
B) \( \mu = 3.8 \)  
C) \( \mu = 3.5 \)  
D) \( \mu = 3.9 \)  

To find the mean, you calculate the expected value by multiplying each outcome by its probability and summing these products.
Transcribed Image Text:**Probability Distribution for a Loaded Die** This example demonstrates a probability distribution for \( x \), where \( x \) is the number that appears when a loaded die is rolled. The distribution is detailed in the following table: | \( x \) | \( P(x) \) | |---------|------------| | 1 | 0.14 | | 2 | 0.16 | | 3 | 0.12 | | 4 | 0.14 | | 5 | 0.13 | | 6 | 0.31 | **Options for the Mean (\( \mu \)) of the Distribution:** A) \( \mu = 0.2 \) B) \( \mu = 3.8 \) C) \( \mu = 3.5 \) D) \( \mu = 3.9 \) To find the mean, you calculate the expected value by multiplying each outcome by its probability and summing these products.
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