Answer to Question #173290 in Statistics and Probability for Denisse Bisuña

Question

The average cholesterol content of a certain canned goods is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed:

a. If a canned goods is selected, what is the probability that the cholesterol content will be greater than 220 milligrams?

b. If a sample of 25 canned goods is selected, what is the probability that the mean of the samle will be larger than 220 milligrams?

Answer 1

a. X ~ $N(215, 15^2)$

$P(X>220) = P(\frac{x-μ}{σ} > \frac{220-215}{15}) \\ = P(Z > 0.333) \\ = 1 -P(Z < 0.333) \\ = 1 -0.6304 \\ = 0.3696 \\ = 36.96 \; \%$

b. n = 25

$P(\bar{X}>220) = 1 -P(X<220) \\ = 1 -P(Z< \frac{x-μ}{\frac{σ}{\sqrt{n}}}) \\ = 1 – P(Z< \frac{220-215}{\frac{15}{\sqrt{20}}}) \\ = 1 -P(Z<1.49) \\ = 1 -0.9318 \\ = 0.068 \\ = 6.82 \; \%$