The number of viewers of American Idol has a mean of 34 million with a standard

Question

The number of viewers of American Idol has a mean of 34 million with a standard deviation of 10 million. Assume this distribution follows a normal distribution.

What is the probability that next week's show will:
  

(a)   Have between 38 and 42 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)
  

Probability  
  

(b)   Have at least 29 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)
  

Probability  
  

(c)   Exceed 54 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)
  

Probability  
  

Explanation / Answer

mean =34 and standard deviation = 10

a) P(38<x<42)=P((38-34)/10<z<(42-34)/10)=P(0.4<z<0.8)=P(z<0.8)-P(z<0.4)

from the normal distribution table, we get 0.7881-0.6554=0.1327

b) P(x>29)=P(z>(29-34)/10)=P(z>-0.5)=P(z<0.5)=0.6915

c) P(x>54)=P(z>(54-34)/10)=P(z>2) =1-P(z<2)=1-0.9772=0.0228

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