Answer to Question #338945 in Statistics and Probability for OLA

Question

The average number of milligrams (mg) of cholesterol in a cup of a certain brand of ice cream is 660 mg, and the standard deviation is 35 mg. Assume the variable is normally distributed.

_______3. If a sample of 10 cups of ice cream is selected, what is the probability that the mean

of the sample will be larger than 670 mg?

A.   11.84%                       B. 14.18%            C. 18.41%           D. 19.41%

_______4. If a sample of 10 cups of ice cream is selected, what is the probability that the mean

of the sample will be smaller than 625 mg?

A.   0.0008%                     B. 0.008%            C. 0.08%             D. 0.8%

_______5. If a sample of 10 cups of ice cream is selected, what is the probability that the mean

of the sample will be larger than 637 mg?

A.   91.28%                       B. 98.12%            C. 98.21%           D. 99.21%

Answer 1

3.

$$P(\bar{X}>670)=1-P(Z\le\dfrac{670-660}{35/\sqrt{10}})$$

$$\approx1-P(Z\le0.903508)\approx0.1831$$

C. 18.41%

4.

$$P(\bar{X}<625)=P(Z<\dfrac{625-660}{35/\sqrt{10}})$$

$$\approx P(Z<-3.16228)\approx0.000783$$

C. 0.08%

5.

$$P(\bar{X}>637)=1-P(Z\le\dfrac{637-660}{35/\sqrt{10}})$$

$$\approx1-P(Z\le-2.07807)\approx0.9811$$

B. 98.12%