Suppose a certain capsule is manufactured so that the dosage of the active ingredient follows the distribution y ~ n(μ = 10 mg, σ = 1 mg). a dosage more than 13mg is considered dangerous. if we sample 49 capsules at random, compute the probability that the mean, y-bar, falls into the dangerous region. pick the closest answer be

So that the means of the sample falls into the dangerous region then

Where is normally distributed with mean  and standar desviation

Then

So:

Finally

.

The probability that the sample mean falls in the dangerous region is approximately zero.

This makes sense, since as the sample size increases, it is less likely to deviate more than 2 standard deviations from the mu population mean.

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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