Question

The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of  12.45 ounces and a standard deviation of  0.30 ounce. Each can holds a maximum of  12.75 ounces of soda. Every can that has more than  12.75 ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the probability that a randomly selected can will need to go through this process?

A. 0.3413

B. 0.1587

C. 0.6587

D. 0.8413

Answer 1

Normal distribution: P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 12.45 ounces

Standard deviation = 0.30 ounce

P(a randomly selected can will need to go through this process) = P(X > 12.75)

= 1 - P(X < 12.75)

= 1 - P(Z < (12.75 - 12.45)/0.30)

= 1 - P(Z < 1)

= 1 - 0.8413

= 0.1587