SOLUTION: 3. The amount of time (in minutes) devoted to commercials on a TV channel during any half-hour program is normally distributed with a mean of 6.3 minutes and a standard deviation

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Question 364371: 3. The amount of time (in minutes) devoted to commercials on a TV channel during any half-hour program is normally distributed with a mean of 6.3 minutes and a standard deviation of 0.866 minutes. What is the probability that a person who watches 20 half-hour programs will see less than 2 hours of commercials?
Answer by robertb(5830) About Me  (Show Source):
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Let X = random variable representing the amount of time (in minutes) devoted to commercials on a TV channel during any half-hour program. Then mu+=+6.3, and sigma+=+0.866. Then Y = 20X is the r.v. representing the amount of time (in minutes) devoted to commercials on a TV channel during 20 half-hour programs. This r.v. is also normally distributed with mean 0.63*20 = 126 minutes, and SD = 20*0.866 = 17.32 minutes. Then P(Y<120) = P(Z< -0.346) = 0.365, approximately.