Answer to Question #336487 in Statistics and Probability for Snow

Question

2. A manufacturer of isopropyl alcohol claims that their product has a mean content of 480 mL. and a standard deviation of 21.5 mL. Assume that the variable is normally distributed. a. If a sample is selected, what is the probability that the content will be less than 505 mL? b. If a sample of 6 isopropyl alcohol is selected, what is the probability that the mean of the sample will be less than 505?

Answer 1

a.

$$P(X<505)=(Z<\frac{505-480}{21.5})$$

$$=P(Z<1.1628)=0.8775$$

b. 

$$P(X<505)=(Z<\frac{505-480}{21.5/\sqrt{6}})$$

$$=P(Z<2.8482)=0.9978$$