Answer to Question #199020 in Statistics and Probability for Nini

Question

 If a sample of 25 canned goods is selected, what is the probability that the mean of the sample will be larger than 20 mg?

Answer 1

Let $X$ be the mean sample: $X\sim N\left(\mu =25,\:\sigma ^2=15^2\right)$ Then,

$Z=\frac{x-\mu }{\sigma }\sim \:N\left(0,1\right)$

The probability that the mean of the sample will be larger than 20mg is:

$X\sim N\left(\mu =25,\:\sigma ^2=15^2\right)$

$=1-P\left(Z\le \frac{25-20}{15}\right)\approx 1-P\left(Z\le 0.3333\right)$

$\approx 0.3694$