The time a song plays on the radio varies from song to song. The time songs play varies according to a normal distribution with mean 3.2 minutes and standard deviation 1.32. What is the probability that a randomly selected song will play longer than 4.5 minutes?

And we can find this probability using the complement rule and we got:

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

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

Where and

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

And we can find this probability using the complement rule and we got:

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

4

step-by-step explanation:

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation: