I only need help with part D. The answer is not 0.001 since that\'s what I thoug
ID: 3057186 • Letter: I
Question
I only need help with part D. The answer is not 0.001 since that's what I thought it was.
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A large playlist consists of songs with times which have mean 3 minutes and standard deviation 10 seconds. a.) A simple random sample of 64 songs is selected. What is the mean of the total length of the 64 songs, in minutes? b.) If as above 64 songs were randomly selected, what is the standard deviation of the total length of the songs, in minutes? (Give decimal answer to two places past decimal.) c.) If length of each of the 64 randomly chosen songs is normally distributed, what is the probability that the total length of the selected songs is less than 189 minutes? Give your answer to 3 places after the decimal. d.) What is the probability that more than 64 randomly chosen songs are required to fill a program which is 196 minutes long? Assume that the length of a randomly selected song is normally distributed. Give your answer to 3 places past the decimal.
Explanation / Answer
a) mean of the total length of the 64 songs =64*3=192
b) standard deviation of the total length of the songs, in minutes =10*(64)1/2 =80
c)
probability that the total length of the selected songs is less than 189 minutes
d
for normal distribution z score =(X-)/ here mean= = 192.000 std deviation == 80.0000