Answer to Question #320159 in Statistics and Probability for Fate

Question

The average number of milligrams of cholesterol in a cup of a certain

brand ice cream is 670 mg and standard deviation is 45 mg, Assume the

variable is normally distributed.

a. If a cup of ice cream is selected, what is the probability that the

cholesterol content will be more than 700 mg?

b. If a sample of 20 cups is selected what is the probability that the mean of

the sample will be larger than 700mg?

Answer 1

$\mu=670,\sigma=45$

a.

$P(X>700)=P(Z>\frac{700-670}{45})$

$=P(Z>0.67)$

$=1-P(Z<0.67)$

$=1-0.7486$

$=0.2514$

b.

$n=20$

$P(X>700)=P(Z>\frac{700-670}{\frac{45}{\sqrt{20}}})$

$=P(Z>2.98)$

$=1-P(Z<2.98)$

$=1-0.9986$

$=0.0014$