Question

If a sample of 25 canned goods is selected, what is the probability that the mean of the sample will be larger than 2210mg?

Answer 1

Let $X=$ the mean of the sample :$X\sim N(\mu=215, \sigma^2=15^2).$ Then $Z=\dfrac{X-\mu}{\sigma}\sim N(0, 1)$

The probability that the mean of the sample will be larger than 220mg is

$$P(X>220)=1-P(X\leq220)=$$

$$=1-P(Z\leq {220-215\over 15})\approx1-P(Z\leq0.3333)\approx$$

$$\approx0.3694$$