Question

Rainbow Punch was made by Frutayuda, Inc. and sold in 12-ounce cans to benefit victims of Hurricane Zero. The mean number of ounces placed in a can by an automatic fill pump is 11.7 with a standard deviation of 0.17 ounce. Assuming a normal distribution, determine the probability that the filling pump will cause an overflow in a can, that is, the probability that more than 12 ounces will be released by the pump and overflow the can.

Answer 1

Answer: Given are following data :

Mean number of ounces filled in a Can = m = 11.7

Standard deviation of ounces filled up in a can = Sd = 0.17

Let , z value for probability that maximum filling will be 12 ounce = Z

Therefore,

m +Z.Sd = 12

Or, 11.7 + 0.17.Z= 12

Or, 0.17.Z 12 – 11.7 = 0.3

Or, Z = 0.3/0.17 = 1.76

Corresponding value of probability for Z = 1.76 as derived from standard normal distribution table = 0.96080

Probability that maximum filling will be 12 ounce= 0.96080

Therefore, more than 12 ounces can be released by the pump

= 1 – Probability that maximum filling will be 12 ounce

= 1 – 0.96080

= 0.0392

PROBABILITY THAT MORE THAN 12 OUNCES CAN BE RELEASED BY THE PUMP = 0.0392