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?

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2022-08-20

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?

Answer & Explanation

Leon Clark

Leon Clark

Beginner2022-08-21Added 9 answers

Mean of the number of viewers in American idol is μ=29 million and the standard deviation is σ=5 million.
Let x be the number of viewers.
X exceeds 40 million
P(X>40)=P(Xμ>40μ)
=P(Xμσ>40μσ)
=P(z>40295)
=P(z>115)
=P(z>2.2)
=0.5-P(0=0.5 - 0.4861 (from Appendix B1.)
=0.0139

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