Suppose that x is normally distributed with mean 110 and standard deviation 30. a. what is the probability that x is greater than 170?

Standard the random variable using the transformation



where and are the mean and standard deviation of , respectively.



Now, you can recall that for any normal distribution, approximately 95% of its data falls within 2 standard deviations of the mean, so to either side, there is approximately 2.5% of data that falls below 2 standard deviations from the mean, and 2.5% that falls above . In other words, .

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