Question

The amount of soda in 16 oz bottles has an unknown distribution with a mean of 16.04 oz and a standard deviation of 0.15 oz. of 36 soda bottles are randomly sample, what is the probability that the mean of this sample is more than the advertised 16 oz?

Answer 1

The applicable formula is;

P(X>16)

Z = (x-mean)/(SD/sqrt (N))

Where;
x = 16 oz
mean = 16.04 oz
SD = 0.15 oz
N = 36 bottles

Substituting;
Z = (16-16.04)/(0.15/Sqrt (36)) = -1.6

Therefore;
P(X>16 oz) = P(Z>-1.6)

From Z-table;
P(Z>-1.6) = 1- P(Z=-1.6) = 1 - 0.0548 = 0.9452 = 94.52%

Therefore, the probability that the sample mean is more than advertised mean is 94.525.