Chocolate bars produced by a certain machine are labeled 8.0 ounces. The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces. A quality control manager initially plans to take a simple random sample of size n from the production line. If he were to double his sample size (to 2n), by what factor would the standard deviation of the sampling distribution of change?

The standard deviation of the sampling distribution would change by a factor of

Step-by-step explanation:

We use the central limit theorem to solve this question.

The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation , a large sample size can be approximated to a normal distribution with mean and standard deviation

In this problem, we have that:

The standard deviation of the population is

Sample size n

Sample size 2n

What factor would the standard deviation of the sampling distribution of change?

So the standard deviation of the sampling distribution would change by a factor of

its a trick question

step-by-step explanation:

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