Questions: 98. A sample of 16 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was two ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce. a. i. x̄= ii. σ= iii. sx= b. In words, define the random variable X. c. In words, define the random variable X̄. d. Which distribution should you use for this problem? Explain your choice.

Transcript text: 98. A sample of 16 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was two ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce. a. i. $\bar{x}=$ $\qquad$ ii. $\sigma=$ $\qquad$ iii. $s_{\mathrm{x}}=$ $\qquad$ b. In words, define the random variable $X$. c. In words, define the random variable $\bar{X}$. d. Which distribution should you use for this problem? Explain vour choice

Solution

Solution Steps

Step 1: Calculate Sample Mean

The sample mean ($ \bar{x} $) is given as: \[ \bar{x} = 2.0 \text{ ounces} \]

Step 2: Identify Population Standard Deviation

The population standard deviation ($ \sigma $) is known to be: \[ \sigma = 0.1 \text{ ounces} \]

Step 3: Identify Sample Standard Deviation

The sample standard deviation ($ s_{\mathrm{x}} $) is provided as: \[ s_{\mathrm{x}} = 0.12 \text{ ounces} \]

Step 4: Define Random Variables

The random variable $ X $ represents the weight of a single small bag of candies: \[ X: \text{Weight of a single small bag of candies} \]

The random variable $ \bar{X} $ represents the mean weight of a sample of 16 small bags of candies: \[ \bar{X}: \text{Mean weight of a sample of 16 small bags of candies} \]

Final Answer

\[ \boxed{ \begin{align_} \text{a. i.} & \quad \bar{x} = 2.0 \\ \text{a. ii.} & \quad \sigma = 0.1 \\ \text{a. iii.} & \quad s_{\mathrm{x}} = 0.12 \\ \text{b.} & \quad X: \text{Weight of a single small bag of candies} \\ \text{c.} & \quad \bar{X}: \text{Mean weight of a sample of 16 small bags of candies} \end{align_} } \]

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