Students drink an average of 05 liters of soda during each p

Students drink an average of 0.5 liters of soda during each presentation at math conferences. The standard deviation is 0.2 liters.

a) What is the probability that a single randomly selected student will consume less than 0.7 liters of soda?

b) I give a presentation and 9 random students show up. What is the probability that the average consumption of these 9 students will be less than 0.7 liters of soda?

Solution

(a) P(X<0.7) = P((X-mean)/s <(0.7-0.5)/0.2)

=P(Z<1) =0.8413 (from standard normal table)

--------------------------------------------------------------------------------------------------------

(b) P(xbar<0.7) = P((xbar-mean)/(s/vn) <(0.7-0.5)/(0.2/sqrt(9)))

=P(Z<3) =0.9987 (from standard normal table)