Math  /  Data & Statistics

QuestionThe acceptable level for insect filth in a certain food item is 4 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 60 ten-gram portions of the food item is obtained and results in a sample mean of xˉ=4.8\bar{x}=4.8 insect fragments per ten-gram portion. Complete parts (a) through (c) below. (a) Why is the sampling distribution of xx approximately normal? A. The sampling distribution of xˉ\bar{x} is approximately normal because the population is normally distributed. B. The sampling distribution of xˉ\bar{x} is approximately normal because the sample size is large enough. C. The sampling distribution of xˉ\bar{x} is assumed to be i.pproximately normal, D. The sampling distribution of xˉ\bar{x} is approximately normal because the population is normally distributed and the sample size is large enough. (b) What is the mean and standard deviation of the sampling distribution of xˉ\bar{x} assuming μ=4\mu=4 and σ=4\sigma=\sqrt{4} ? μx=\mu_{x}= \square (Round to three decimal places as needed.) Get more help - Clear all Check answer

Studdy Solution
The standard deviation of the sampling distribution of xˉ\bar{x}, also known as the standard error, is calculated using the formula:
σxˉ=σn\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}
Substitute the given values:
σxˉ=2600.258\sigma_{\bar{x}} = \frac{2}{\sqrt{60}} \approx 0.258
The mean of the sampling distribution of xˉ\bar{x} is μxˉ=4 \mu_{\bar{x}} = 4 .
The standard deviation of the sampling distribution of xˉ\bar{x} is σxˉ0.258 \sigma_{\bar{x}} \approx 0.258 .

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