Example 1

Suppose my iPod has 3,000 songs. The histogram below shows the distribution of the lengths of these songs. We also know that, for this iPod, the mean length is 3.45 minutes and the standard deviation is 1.63 minutes. Calculate the probability that a randomly selected song lasts more than 5 minutes.

pnorm(5,mean=3.45, sd=1.63, lower.tail = FALSE)
## [1] 0.1708224

Example 2

I’m about to take a trip to visit my parents and the drive is 6 hours. I make a random playlist of 100 songs. What is the probability that my playlist lasts the entire drive?

#6hours->360minutes->mean of 100 songs = 3.6
#The question is: what is the probability of mean of 100 randomly selected songs is more than 3.6

pnorm(3.6,mean=3.45, sd=1.63/sqrt(100), lower.tail = FALSE)
## [1] 0.1787223