16. ppose that the very pop song length in America is minutes with standard devi

Question

16. ppose that the very pop song length in America is minutes with standard deviation of minutes. Ris known that sorg length is not normally debuted. Suppeandom sample of 25 songs taken from the population. Show your work for alleredit. What is the approximate probability that the average song length will be less than 15 minutest Round to the nearest thousaneth. Use Tatie in Appendix to solve this problem. find the probably that a singe randomly selected song from the population will longer than minute Round to the nearest thousand. Use Table in Appendix to solve this problem.

Explanation / Answer

P(X < 3.5) = P((X - mean)/(SD/sqrt (n)) < (3.5 - mean)/(SD/sqrt(n))

= P(Z < (3.5 - 4)/(1.25/sqrt(25))

= P(Z < -2)

= 0.0228

B) P(X > 4.15) = P((X - mean)/SD) > (3.5 - mean)/SD)

= P(Z > (4.15 - 4)/1.25)

= P(Z > 0.12)

= 1 - P(Z < 0.12)

= 1 - 0.5478

= 0.4522

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