Answer:
32.64%
Step-by-step explanation:
Let's define the random variable X in the following way:
X: the volume of a soda in a quart soda bottle. We know that X is normally distributed with a mean of 32 ounces and a standard deviation of 1.2 ounces, i.e.,
= 32 ounces
= 1.2 ounces
The normal density function for a random variable with a mean of 32 and a standard deviation of 1.2 is given by
![f(x)=\frac{1}{\sqrt{2\pi }1.2} \exp[-\frac{(x-32)^{2} }{2(1.2)^2} ]](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B2%5Cpi%20%7D1.2%7D%20%5Cexp%5B-%5Cfrac%7B%28x-32%29%5E%7B2%7D%20%7D%7B2%281.2%29%5E2%7D%20%5D)
and we need to calculate the following probability
, this probability is given by
= 0.3263552
you can use a computer to calculate this probability or a table from a book. You can use the following instruction in the R statistical programming language for example
pnorm(31.46, mean = 32, sd = 1.2) with give us 0.3263552, then,
the percentage we are looking for is (0.3263552)(100)=32.64.