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 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?  147

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.)

1.1700

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 145 minutes? Give your answer to 3 places after the decimal.

0.0440

d.) What is the probability that more than 49 randomly chosen songs are required to fill a program which is 151 minutes long? Assume that the length of a randomly selected song is normally distributed. Give your answer to 3 places past the decimal.

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Explanation / Answer

d)

for normal distribution z score =(X-)/ here mean=       = 147.000 std deviation   == 1.17 sample size       =n= 1 std error=x=/n= 1.1667 probability = P(X>151) = P(Z>3.43)= 1-P(Z<3.43)= 1-0.9997= 0.0003~0.000

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