In this activity, we investigate the sampling distribution of the sample mean, X 1. Imagine that you roll a single, fair, six-sided die once. Define the random variable X, to be the number of dots (pips) on the upward face. Complete the probability distribution table for X. P(x) 1 3 4. 5 2. Sketch the probability histogram for X below. Let the x-axis be the OUTCOME and let the y-axis be the PROBABILITY. 3. Determine the mean and standard deviation for X. As a reminder, you determine the mean of a discrete probability distribution using u=ExP(x) and the standard deviation is found most simply using the formula o = \EײP(x)– µ² (see page 322).

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In this activity, we investigate the sampling distribution of the sample mean, \(\bar{X}\).

### 1. Probability Distribution

Imagine that you roll a single, fair, six-sided die once. Define the random variable \(X\) to be the number of dots (pips) on the upward face. Complete the probability distribution table for \(X\).

| x | P(x) |
|---|------|
| 0 |      |
| 1 |      |
| 2 |      |
| 3 |      |
| 4 |      |
| 5 |      |
| 6 |      |

### 2. Histogram

Sketch the probability histogram for \(X\) below. Let the x-axis be the OUTCOME and let the y-axis be the PROBABILITY.

(Blank graph for sketching with labeled axes, x-axis labeled "Outcome" and y-axis labeled "Probability")

### 3. Mean and Standard Deviation

Determine the mean and standard deviation for \(X\). As a reminder, you determine the mean of a discrete probability distribution using:

\[
\mu = \sum xP(x)
\]

and the standard deviation is found most simply using the formula:

\[
\sigma = \sqrt{\sum x^2P(x) - \mu^2}
\]

(see page 322).
Transcribed Image Text:In this activity, we investigate the sampling distribution of the sample mean, \(\bar{X}\). ### 1. Probability Distribution Imagine that you roll a single, fair, six-sided die once. Define the random variable \(X\) to be the number of dots (pips) on the upward face. Complete the probability distribution table for \(X\). | x | P(x) | |---|------| | 0 | | | 1 | | | 2 | | | 3 | | | 4 | | | 5 | | | 6 | | ### 2. Histogram Sketch the probability histogram for \(X\) below. Let the x-axis be the OUTCOME and let the y-axis be the PROBABILITY. (Blank graph for sketching with labeled axes, x-axis labeled "Outcome" and y-axis labeled "Probability") ### 3. Mean and Standard Deviation Determine the mean and standard deviation for \(X\). As a reminder, you determine the mean of a discrete probability distribution using: \[ \mu = \sum xP(x) \] and the standard deviation is found most simply using the formula: \[ \sigma = \sqrt{\sum x^2P(x) - \mu^2} \] (see page 322).
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