Question

A machine at Pepco Inc that fills soft drink cans advertised to contain 12 oz of soft drink actually dispenses a volume (V) per can that is normally distributed with mean 11.8 oz and standard deviation 0.2 oz. Government regulations require that at least 99% of the cans advertised as containing 12 oz of soft drink actually contain 11.6 oz or more. Quality control statisticians are hired to use probability to design quality control experiments that constantly monitor the filling process to guarantee that this regulation is respected. The departure from 12 oz is due to chance. The quality control statistician is not there to make the volume exactly 12 oz but to make sure that there are no systematic departures from it, such as always overfilling or always underfilling, which would indicate that the machine is broken.

Required:
a. Suppose that you are the inspector for the Government regulatory agency. Is Pepco Inc following government regulations?
b. Pepco Inc. is a multinational with 1000 branches all over the world. All their filling machines are as described in part (a). What is the probability that more than 700 of these machines a randomly chosen can contains less than 11.6 oz of soft drink?

Answer 1

a). No, Pepco Inc. do not follow the regulations of the government as at least 99% of the cans that are advertised contains 12 oz of the soft drinks actually contains 11.6 oz or more than that.

b). The probability of having more than 700 of the machines at randomly chosen contains less than 11.6 oz of the soft drinks is -15.87%.

Explanation:

It is given that :

Mean,
`$\mu = 11.8 $`

Standard deviation,
`$\sigma = 0.2$`

Thus we have to compute
`$Pr(X \leq 11.6)$`.

The corresponding z - value to be computed is :

`$Z = (X - \mu)/(\sigma)$`

`$Z = (11.6-11.8)/(0.2)$`

= -1

Therefore,

`$Pr(X \leq 11.6)$`
`$=Pr(Z \leq (11.6-11.8)/(0.2))$`

`$=Pr(Z \leq -1)$`

= 0.1587

Now, as stated the government regulations requires that at least 99% of the cans that are advertised contains 12 oz of the soft drinks actually contains 11.6 oz or more. However we can compute tha there are as large as 15.87% of the total cans having soft drinks below 11.6 oz.

Thus, it means only 84% approx. of the cans have soft drinks more than 11.6 oz.

Therefore we conclude that Pepco Inc does not follow government regulations of keeping the amount of soft drink at least 11.6 oz.