A large playlist consists of songs with times which have a mean of 4 minutes and a standard deviation of 10 seconds.
a.) A simple random sample of 49 songs is selected. What is the mean of the total length of the 49 songs, in minutes?
b.) If, as above, 49 songs were randomly selected, what is the standard deviation of the total length of the songs, in minutes? (Give the decimal answer to two places past the decimal.)
c.) If the length of each of the 49 randomly chosen songs is normally distributed, what is the probability that the total length of the selected songs is less than 194 minutes? Give your answer to 3 decimal places.
d.) What is the probability that more than 49 randomly chosen songs are required to fill a program that is 200 minutes long? Assume that the length of a randomly selected song is normally distributed. Give your answer to 3 decimal places.