Questions: If the mean of a random variable X is 55, what will be the mean of the sampling distribution of the sample mean? μx̄ = □

Transcript text: (b) If the mean of a random variable X is 55 , what will be the mean of the sampling distribution of the sample mean? \[ \mu_{\overline{\mathrm{x}}}=\square \]

Solution

Solution Steps

To find the mean of the sampling distribution of the sample mean, we use the property that the mean of the sampling distribution of the sample mean is equal to the mean of the population from which the samples are drawn. Therefore, if the mean of the random variable \( X \) is 55, then the mean of the sampling distribution of the sample mean is also 55.

Step 1: Identify the Given Information

We are given that the mean of a random variable \( X \) is 55. This is denoted as \( \mu_X = 55 \).

Step 2: Apply the Property of the Sampling Distribution

The mean of the sampling distribution of the sample mean, denoted as \( \mu_{\overline{X}} \), is equal to the mean of the population from which the samples are drawn. Therefore, \( \mu_{\overline{X}} = \mu_X \).

Step 3: Calculate the Mean of the Sampling Distribution

Since \( \mu_X = 55 \), it follows that \( \mu_{\overline{X}} = 55 \).