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post16 - STAT 511-2 Spring 2012 Lecture 16 Jun Xie 4.3 The...

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1 STAT 511-2 Spring 2012 Lecture 16 Feb 17, 2012 Jun Xie 4.3 The normal distribution Example 16 Reaction time for an in-traffic response to a brake signal from standard brake lights can be modeled with a normal distribution having mean value 1.25 sec and standard deviation of .46 sec. What is the probability that reaction time is between 1.00 sec and 1.75 sec? Example 18 The amount of distilled water dispensed by a certain machine is normally distributed with mean value 64 oz and standard deviation .78 oz. What container size c will ensure that overflow occurs only .5% of the time? If X denotes the amount dispensed, the desired condition is that P ( X > c ) = .005, or, equivalently, that P ( X c ) = .995. The 99.5th percentile of the standard normal distribution is 2.58, so c = (.995) = 64 + (2.58)(.78) = 64 + 2.0 = 66 oz. Go over the homework problems Page 162, 42 and 44. Normal distribution approximating the binomial distribution A normal curve with =np and =sqrt(np(1-p)) has been superimposed on the probability histogram of binomial Bin(20,.6).

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