Questions: Multiple Choice: Select the correct answer from the options provided below. Given the following probability distribution, is 1 considered an unusual value for the random variable x? In other words, is 1 unusually low? x P(3) 0 0.10 1 0.05 2 0.36 3 0.34 4 0.15 The value x=1 [Select] considered unusual because [Select]

Multiple Choice: Select the correct answer from the options provided below.

Given the following probability distribution, is 1 considered an unusual value for the random variable x? In other words, is 1 unusually low?

x P(3)
0 0.10
1 0.05
2 0.36
3 0.34
4 0.15

The value x=1 [Select] considered unusual because [Select]

Transcript text: Multiple Choice: Select the correct answer from the options provided below. Given the following probability distribution, is 1 considered an unusual value for the random variable $x$ ? In other words, is 1 unusually low? \begin{tabular}{|c|c|} \hline$x$ & $P(3)$ \\ \hline 0 & 0.10 \\ \hline 1 & 0.05 \\ \hline 2 & 0.36 \\ \hline 3 & 0.34 \\ \hline 4 & 0.15 \\ \hline \end{tabular} The value $x=1$ [Select] $\square$ considered unusual because [Select] $\square$

Solution

Solution Steps

To determine if a value is considered unusual in a probability distribution, we typically look at the probability associated with that value. A common rule of thumb is that a value is considered unusual if its probability is less than 0.05. In this case, we will check if the probability of $ x = 1 $ is less than 0.05.

Step 1: Identify the Probability of $ x = 1 $

The probability distribution provided is: \[ \begin{array}{|c|c|} \hline x & P(x) \\ \hline 0 & 0.10 \\ 1 & 0.05 \\ 2 & 0.36 \\ 3 & 0.34 \\ 4 & 0.15 \\ \hline \end{array} \] The probability of $ x = 1 $ is $ P(1) = 0.05 $.

Step 2: Determine if $ x = 1 $ is Unusual

A value is typically considered unusual if its probability is less than 0.05. Here, $ P(1) = 0.05 $.

Step 3: Conclusion

Since $ P(1) = 0.05 $ is not less than 0.05, the value $ x = 1 $ is not considered unusual.