A large playlist consists of songs with times which have mean 3 minutes and stan

Question

A large playlist consists of songs with times which have mean 3 minutes and standard deviation 15 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? 3 Submit Answer Incorrect. Tries 1/5 Previous Tries b.) If as above 49 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.) 2.14 Submit Answer Incorrect. Tries 1/5 Previous Tries c.) If 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 144 minutes? Give your answer to 3 places after the decimal. 0.489 Submit Answer Incorrect. Tries 1/5 Previous Tries d.) What is the probability that more than 49 randomly chosen songs are required to fill a program which is 152 minutes long? Assume that the length of a randomly selected song is normally distributed. Give your answer to 3 places past the decimal. 0.519 Submit Answer Incorrect. Tries 1/5 Previous Tries

Explanation / Answer

Soution:-

a) n = 49*3 =  147

b) V[T] = 49(1/7)2 = 1 => 2 = 1

c) P(T < 144) = P(Z < (144 147)/1) = P(Z < 3) =0.0013 = 0.001

d) P(T < 152) = P(Z < (152 147)/1) = P(Z < 5) = 0.999 = 1.000

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