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. If 36 soda bottles are randomly sampled, what is the probability that the mean of this sample is more than the advertised 16 OZ?

Answer 1

Explanation:

Given that 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.

Sample size n =36; std error = std dev/sqrt n

=
`(0.15)/(√(36) ) \\=0.025`

Mean diff = 16.04-16 =0.04

Test statistic = Mean diff/SE = 1.6

P(X>16) = P(Z>1.6) = 0.5-0.4452

=0.0548