Question

NewPop produces their brand of soda drinks in a factory where they claim that the mean volume of the bottles is 24 ounces with a standard deviation of .14 ounces. Part A: If 22,000 bottles are filled each day, how many bottles are within 14 ounces of the mean? Part B: Bottles are rejected if they contain less than 23.72 ounces. How many bottles would you expect to be rejected in a sample of 22,000 bottles?

Answer 1

a) 14960 bottles

b) 502 bottles

Explanation:

Given that:

Mean (μ) = 24 ounces, standard deviation (σ) = 0.14 ounces

a) From empirical rule (68−95−99.7%) , 68% of the population are within 1 standard deviation of the mean i.e within μ ± 1σ.

Therefore, the number of bottles filled 0.14 ounces of the mean = 22,000*68% = 14960 bottles

b) since it contains less than 23.72, we can use the z score formula where x = 23.72

`z=(x-\mu)/(\sigma)=(23.72-24)/(0.14) =-2`

From the normal probability distribution table: P(X < 23.72) = P (Z < -2) = 0.0228

The number of rejected bottles = 22000 × 0.0228 = 502 bottles