Please show all the work, and do it by typing on the computer Thank you, you onl

Question

Please show all the work, and do it by typing on the computer Thank you, you only need to answer no.4

The length in minutes of Daft Punk songs (call this D) are approximately Normally distributed with a mean of 4.125 minutes and a variance of 1.2769.

1.       What is the probability that a Daft Punk song is at least 2.8 minutes long? (3 points)

2.       If you know that the next song in your Daft Punk playlist is shorter than 5.8 minutes long, what is the probability it is longer than 4 minutes? (4 points)

3.       The song Voyager is 3.5 minutes long. Is this song in the shortest 40% of Daft Punk songs? (4 points)

  Show the work to verify your answer

4.       The local radio station pays royalties for each song it plays. The rate for a Daft Punk song is $0.024 times the length (in minutes) of the song. What is the average royalty payment and the standard deviation of the royalty payment of a Daft Punk song?   (4 points)

Explanation / Answer

D - N(4.125,1.2769)

sd = sqrt(var) = sqrt(1.2769) = 1.13

Z = (D - 4.125)/1.13

Y - royalty payment

Y = 0.024*D

E(Y) = E(0.024*D) = 0.024*E(D)

= 0.024 * 4.125 = 0.099

sd(Y) = sd (0.024*D)= 0.024* sd(D)

= 0.024 * 1.13

= 0.02712

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

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