Solution :
The length (in seconds) of 80 of U2 (an Irish band) songs were selected at random.
From the data given , we have the following information about different measures (C).
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(e) We assume that the given data is normally distributed and that the band's entire collection of songs has a mean and standard deviation equal to those calculated above.
We have to find out the percentage of U2 songs that are expected to be the following:
(i) Over 180 seconds : Thus , we have to find P (X > 180)
Thus, the percentage of U2 songs that are expected to be over 180 seconds = 86.842 % ... (Ans)
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(ii) Between 210 seconds and 300 seconds : Thus , we have to find P (210 < X < 300)
Thus, the percentage of U2 songs that are expected to be between 210 seconds and 300 seconds = 43.141 % ................... (Ans)
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(f) To find the length of time (in seconds) under which 90% of the U2 songs are expected to be :
Let the length of time (in seconds) of the U2 songs be
.
Let the length of time (in seconds) under which there
are 90% of the U2 songs be ""
Thus , clearly we have to find ""
such that , P ( X < x ) = 0.90.
The length of time under which 90% of the U2 songs are expected to be = 367.1527 secs ...(Ans)
...Values of Range and Standard Deviation are given at the first ...
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