Question

The times to pop a 3.4-ounce bag of microwave popcorn without burning it are Normally distributed with a mean

Answer 1

This question is solved using the central limit theorem, giving an answer of:

Fourth option, approximately normal with mean of 140 seconds and standard deviation of 10 seconds.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 140, standard deviation of 20, sample of 4:

By the Central Limit Theorem, the distribution is approximately normal.

Mean is the same, of 140.

$n = 4, \sigma = 20$, thus:

$s = \frac{\sigma}{\sqrt{n}} = \frac{20}{\sqrt{4}} = 10$

Thus, the correct answer is:

Fourth option, approximately normal with mean of 140 seconds and standard deviation of 10 seconds.

For another example of the Central Limit Theorem, you can check brainly.com/question/15519207