Answer to Question #192373 in Statistics and Probability for gabrielle

Question

the average cholesterol content of a certain canned goods is 215 milligram and the standard deviation is 15 milligram, answer the variable is normally distributed

Answer 1

The complete question is :

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:

a.) $P(X>220) = P(\dfrac{x- \mu}{\sigma}>\dfrac{220-215}{15})$

$= P(Z>0.333)$

$= 1-P(Z<0.333)$

$= 1-0.6304$

$= 0.369$

b.) We have $n = 25$

$P(\bar X >220) = 1-P(X<220)$

$= 1-P(Z<\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}})$

$= 1-P(Z< \dfrac{220-215}{\dfrac{15}{\sqrt{20}}})$

$= 1-P(Z<1.49)$

$= 1-0.9318$

$= 0.068$