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 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

=64*3 =192

=10/60 =1/6 =0.1666

a) sample mean,x = =192

b)

standard deviation,x =n =0.166664

                                           =0.1666*8

                                           =1.33

c)

x=189

z=(x-)/(x)

=(189-192)/1.33

=-3/1.33

=-2.25

P(x<189) =P(z<-2.25)

              =0.012

d)

x=189

z=(x-)/(x)

=(196-192)/1.33

=4/1.33

=3.01

P(x>196) =P(z>3.01)

              =1-P(z<3.01)

              =1-0.9987

              =0.001

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.