Question

Parking concerns ~ Over the years, parking has become an issue during spring at MSU as more people bring cars to campus. The waiting time to find a parking spot at Wells Hall parking lot is normally distributed with an average of 10 minutes and a standard deviation of 3.6 minutes during peak hours (10 am – 5 pm). What proportion of waiting times are between 8 and 12 minutes? Enter your answer to 4 decimal places.

Answer 1

Answer:

$P(8$

And we can find this probability with this difference:

$P(-0.56$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

$P(-0.56$

Step-by-step explanation:

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 waiting time of a population, and for this case we know the distribution for X is given by:

$X \sim N(10,3.6)$  

Where $\mu=10$ and $\sigma=3.6$

We are interested on this probability

$P(8$

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:

$P(8$

And we can find this probability with this difference:

$P(-0.56$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

$P(-0.56$