Crave Creamery is an ice cream shop chain that has locations all across the nation. Customers at Crave Creamery have the option of ordering I, 2 , or 3 scoops
of ice cream in their cone. The mean number of scoops ordered is , with a standard deviation of . Suppose that we will taice a random sample
of ice cream cone orders and record the number of scoops for each. Let represent the sample mean of the number of scoops for the 7 ice cream cone
orders. Consider the sampling distribution of the sample mean .
Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed.
(a) Find (the mean of the sampling distribution of the sample mean).
(b) Find (the standard deviation of the sampling distribution of the sample mean).
(b)

Ask by Mann Black. in the United States

Mar 25,2025

Question

Crave Creamery is an ice cream shop chain that has locations all across the nation. Customers at Crave Creamery have the option of ordering I, 2 , or 3 scoops
of ice cream in their cone. The mean number of scoops ordered is , with a standard deviation of . Suppose that we will taice a random sample
of ice cream cone orders and record the number of scoops for each. Let represent the sample mean of the number of scoops for the 7 ice cream cone
orders. Consider the sampling distribution of the sample mean .
Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed.
(a) Find (the mean of the sampling distribution of the sample mean).
(b) Find (the standard deviation of the sampling distribution of the sample mean).
(b)

Ask by Mann Black. in the United States

Mar 25,2025

UpStudy AI · Accepted Answer

**(a) Calculating $$ \mu_{\bar{x}} $$:**

The mean of the sampling distribution of the sample mean is the same as the population mean:
$$
\mu_{\bar{x}} = \mu = 2.86
$$

**(b) Calculating $$ \sigma_{\bar{x}} $$:**

The standard deviation of the sampling distribution (also known as the standard error) is calculated by:
$$
\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{0.23}{\sqrt{7}}
$$

Calculating $$\sqrt{7}$$:
$$
\sqrt{7} \approx 2.65
$$

Then:
$$
\sigma_{\bar{x}} \approx \frac{0.23}{2.65} \approx 0.09
$$

Thus, the answers are:

(a) $$ \mu_{\bar{x}} = 2.86 $$

(b) $$ \sigma_{\bar{x}} \approx 0.09 $$
**(a) $$ \mu_{\bar{x}} = 2.86 $$ **(b) $$ \sigma_{\bar{x}} = 0.09 $$**

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