The number of viewers of American Idol has a mean of 29 million with a standard deviation of 5 million. Assume this distribution follows a normal distribution. What is the probability that next week’s show will:

Exceed 40 million viewers?

Exceed 40 million viewers?

1 Answers

Best Answer

Mean of the number of viewers in American idol is mu = 29 million and the standard deviation is sigma = 5 million.
Let x be the number of viewers.
X exceeds 40 million
P(X>40)=P(X- mu > 40- mu)
=P((X- mu)/(sigma)> (40- mu)/(sigma))
=P(z> (40-29)/(5))
=P(z> (11)/(5))
=P(z>2.2)
=0.5-P(0<z<2.2)
=0.5 - 0.4861 (from Appendix B1.)
=0.0139