Question

The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles can we expect to have a volume less than 32 oz?

Answer 1

Answer: We can expect about 40.13% of bottles to have a volume less than 32 oz.

Step-by-step explanation:

Given : The volumes of soda in quart soda bottles can be described by a Normal model with

$\mu=\text{32.3 oz}\\\\\sigma=\text{1.2 oz}$

Let X be the random variable that represents the volume of a randomly selected bottle.

z-score :$\dfrac{x-\mu}{\sigma}$

For x = 32 oz

$z=\dfrac{32-32.3}{1.2}=-0.25$

The probability of bottles have a volume less than 32 oz is given by :-

$P(X<32)=P(z<-0.25)=0.4012937$           [Using standard normal table]

In percent, $0.4012937\times100=40.12937\%\approx40.13\%$

Hence, we can expect about 40.13% of bottles to have a volume less than 32 oz.