Question

A soft drink machine outputs a mean of 24 ounces per cup. The machine's output is normally distributed with a standard deviation of 3 ounces. What is the probability of filling a cup between 21 and 28 ounces? Round your answer to four decimal places.

Answer 1

Answer:

$P(21$

And we can find the probability with this difference

$P(-1$

And using the normal standard distribution or excel we got:

$P(-1$

Step-by-step explanation:

Let X the random variable that represent the soft drink machine outputs of a population, and for this case we know the distribution for X is given by:

$X \sim N(24,3)$  

Where $\mu=24$ and $\sigma=3$

We want to find this probability:

$P(21$

The z score is given by:

$z=\frac{x-\mu}{\sigma}$

Using this formula we got:

$P(21$

And we can find the probability with this difference

$P(-1$

And using the normal standard distribution or excel we got:

$P(-1$