A large playlist consists of songs with times which have mean 2 minutes and standard deviation 10 seconds.
What is the probability that more than 64 randomly chosen songs are required to fill a program which is 132 minutes long? Assume that the length of a randomly selected song is normally distributed.
My mean for the total length of 64 randomly chosen songs is 128 minutes.
The standard deviation for the total length of 64 songs is 4/3 minutes.
I have tried using z-scores to calculate this. (132-128)/(4/3) = 3. Then I did 1 - F(3) = 0.0013, which was wrong.
I'm confused as to where I went wrong.
Thank you for any help!