SOLUTION: If the random variable z is the standard normal score, is it right that P(z>5) could easily be approximated without referring to a table? Why or why not?

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Question 458587: If the random variable z is the standard normal score, is it right that P(z>5) could easily be approximated without referring to a table? Why or why not?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

answered by: robertb(3361)
The standard normal curve has a few neat properties that make it convenient to use. (Aside from its being a benchmark for all computations involving any normal distribution.) Among them are its zero mean and standard deviation of 1. There is the 68-95-99.7 rule, which says that 68% of the observations fall between -1 and 1 (within 1 standard deviation of the mean of 0), 95% fall between -2 and 2 (within 2 standard deviations of the mean) and 99.7% fall between -3 and 3 (within 3 standard deviations of the mean). Thus, P(-1 < z <1) = 0.68, P(-2 < z< 2) = 0.95, and P(-3 < z <3) = 0.997. You don't need a standard normal table for these. =)