Questions: Crave Creamery is an ice cream shop chain that has locations all across the nation. Customers at Crave Creamery have the option of ordering 1,2 , or 3 scoops of ice cream in their cone. The mean number of scoops ordered is μ=1.30, with a standard deviation of σ=0.68. Suppose that we will take a random sample of n=10 ice cream cone orders and record the number of scoops for each. Let x̄ represent the sample mean of the number of scoops for the 10 ice cream cone orders. Consider the sampling distribution of the sample mean x̄. Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed. (a) Find μx̄ (the mean of the sampling distribution of the sample mean). μx̄= (b) Find σx̄ (the standard deviation of the sampling distribution of the sample mean). σx̄=

Crave Creamery is an ice cream shop chain that has locations all across the nation. Customers at Crave Creamery have the option of ordering 1,2 , or 3 scoops of ice cream in their cone. The mean number of scoops ordered is μ=1.30, with a standard deviation of σ=0.68. Suppose that we will take a random sample of n=10 ice cream cone orders and record the number of scoops for each. Let x̄ represent the sample mean of the number of scoops for the 10 ice cream cone orders. Consider the sampling distribution of the sample mean x̄. Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed. (a) Find μx̄ (the mean of the sampling distribution of the sample mean). μx̄= (b) Find σx̄ (the standard deviation of the sampling distribution of the sample mean). σx̄=
Transcript text: Crave Creamery is an ice cream shop chain that has locations all across the nation. Customers at Crave Creamery have the option of ordering 1,2 , or 3 scoops of ice cream in their cone. The mean number of scoops ordered is $\mu=1.30$, with a standard deviation of $\sigma=0.68$. Suppose that we will take a random sample of $n=10$ ice cream cone orders and record the number of scoops for each. Let $\bar{x}$ represent the sample mean of the number of scoops for the 10 ice cream cone orders. Consider the sampling distribution of the sample mean $\bar{x}$. Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed. (a) Find $\mu_{\bar{x}}$ (the mean of the sampling distribution of the sample mean). \[ \mu_{\bar{x}}= \] $\square$ (b) Find $\sigma_{\bar{x}}$ (the standard deviation of the sampling distribution of the sample mean). \[ \sigma_{\bar{x}}= \] $\square$
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Solution

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Solution Steps

Step 1: Mean of the Sampling Distribution

The mean of the sampling distribution of the sample mean \( \mu_{\bar{x}} \) is equal to the population mean \( \mu \). Therefore, we have:

\[ \mu_{\bar{x}} = \mu = 1.30 \]

Step 2: Standard Deviation of the Sampling Distribution

The standard deviation of the sampling distribution of the sample mean \( \sigma_{\bar{x}} \) is calculated using the formula:

\[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \]

Substituting the given values:

\[ \sigma_{\bar{x}} = \frac{0.68}{\sqrt{10}} \approx 0.2155 \]

Rounding to two decimal places, we find:

\[ \sigma_{\bar{x}} \approx 0.22 \]

Final Answer

\[ \mu_{\bar{x}} = 1.30, \quad \sigma_{\bar{x}} = 0.22 \]

Thus, the final boxed answers are:

\[ \boxed{\mu_{\bar{x}} = 1.30} \] \[ \boxed{\sigma_{\bar{x}} = 0.22} \]

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