Question

A regulation hockey puck must weigh between 5.5 and 6 ounces. The weights X of pucks made by a particular process are normally distributed with mean 5.75 ounces and standard deviation 0.11 ounce. Find the probability that a puck made by this process will meet the weight standard.

Answer 1

Answer:

$P(5.5$

And we can find this probability with this difference:

$P(-2.27$

Step-by-step explanation:

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

$X \sim N(5.75,0.11)$  

Where $\mu=5.75$ and $\sigma=0.11$

We are interested on this probability

$P(5.5$

And we can use the z score formula given by:

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

If we apply this formula to our probability we got this:

$P(5.5$

And we can find this probability with this difference:

$P(-2.27$