Suppose the length of a song is normally distributed with a

Suppose the length of a song is normally distributed with a mean time of 227 seconds and a standard deviation of 31.5 seconds. Suppose we take a sample of 30 songs from itunes top 100 songs.

                a. What is the probability that the song will last between 3.5 and 3.75 minutes?

Solution

see mean is 227 that is 3mins 47 seconds

standard deviation is 31.5 seconds, now 3mins 47 sec - 31.5 sec = 3mins 15.5 sec

3 mins 47 sec + 31.5 sec =4 min 18.5 sec

sample of 30 among 100

as the values are in the finding range therefore we can directly say that the probability will be 30/100 = 0.3