Answer to Question #238546 in Statistics and Probability for Phindile

Question

A Coca-Cola machine is made in such a way that it dispenses 500ml of coke per pet bottle drink. Suppose it is known that the amount of coke dispensed follows a normal distribution with mean 500 and variance 400.

a) You enter a spaza shop where you take a 500 ml bottle of coke from the fridge to drink at the premises. What is the probability that the bottle you select contain more than 550 ml of coke? (4)

b) Belowhowmanymillilitresdoyouget25%ofthedrinks? (5)

c) Suppose you further select, nine of the 500 ml bottles of coke from the fridge to bring your relatives at home. What is the probability that the all the nine bottles contain at least 4950 ml of coke? (5)

d) What is the probability that the mean contents of the selected nine bottles will be at least 440ml and at most 520 ml. (6)

e) Below what mean value do you find 25% of the sampled average content? (5)