Question

The pucks used by the National Hockey League for ice hockey must weigh between and ounces. Suppose the weights of pucks produced at a factory are normally distributed with a mean of ounces and a standard deviation of ounces. What percentage of the pucks produced at this factory cannot be used by the National Hockey League? Round your answer to two decimal places.

Answer 1

Answer:

$P(5.5$

And we can find this probability using the normal standard distribution or excel and we got:

$P(-2.769$

Step-by-step explanation:

For this case we assume the following complete question: "The pucks used by the National Hockey League for ice hockey must weigh between 5.5 and 6 ounces. Suppose the weights of pucks produced at a factory are normally distributed with a mean of 5.86 ounces and a standard deviation of 0.13ounces. What percentage of the pucks produced at this factory cannot be used by the National Hockey League? Round your answer to two decimal places. "

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

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:

$X \sim N(5.86,0.13)$  

Where $\mu=5.86$ and $\sigma=0.13$

We are interested on this probability

$P(5.5$

And the best way to solve this problem is using the normal standard distribution and the z score 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 using the normal standard distribution or excel and we got:

$P(-2.769$