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 = □

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? \[ \mu_{\overline{\mathrm{x}}}=\square \]
failed

Solution

failed
failed

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 \( \mu_{\overline{X}} = 55 \).

Final Answer

The mean of the sampling distribution of the sample mean is \(\boxed{55}\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Find the compound amount on a deposit of 7610 at 9% for 8 years by multiplying the original amount deposited by 100% plus the compound rate. The compound amount is . (Round to the nearest hundredth.)
failedAnswered
Assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are n=8 trials, each with probability of success (correct) given by p=0.45. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4 P(X<4)= (Round to four decimal places as needed.)
failedAnswered
Work with a partner. Take turns drawing one cube from the bag and placing it on your page in the rectangle of the same color. When the bag is empty, do I can ... you have more red or blue cubes? How do you know? Draw a picture of your cubes in the rectangles showing which group has more. Compare the number of objects from 0 to 20 in two groups using the terms less than, equal to or greater than.
failedAnswered
Describe what fixed costs and marginal costs mean to a company. Choose the correct answer below. A. Fixed cost is the constant for a particular product and does not change as more items are made. Marginal cost is the rate of change of cost C(x) at the level of production x and is equal to the slope of the cost function at x. B. Fixed cost is the rate of change of cost C(x) at the level of production x and is equal to the slope of the cost function at x. Marginal cost is the constant for a particular product and does not change as more items are made. C. The number of units at which revenue just equals cost is the fixed cost. Marginal cost is the constant for a particular product and does not change as more items are made. D. Fixed cost is the constant for a particular product and does not change as more items are made. The number of units at which revenue just equals cost is the marginal cost.
failedAnswered
The text does not contain any content related to a specific question, only placeholders for equations that are not provided.