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: Have at least 23 million viewers?

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2022-08-18

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:
Have at least 23 million viewers?

Answer & Explanation

Simekr7

Simekr7

Beginner2022-08-19Added 6 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 is at least 23 million
P(X>23)=P(Xμ>23μ)
=P(Xμσ>23μσ)
=P(z>23295)
=P(z>65)
=P(z>-1.2)
=P(z<1.2)
=0.5+P(0=0.5 + 0.3849 (from Appendix B1.)
=0.8849

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