A quick approximation is sometimes useful when an exact answer is not required.
ID: 3375512 • Letter: A
Question
A quick approximation is sometimes useful when an exact answer is not required. (a) Verify the statements in the Empirical Rule for the normal probability density function with ? = 5.1 and ? = 8.374.
(a) P(? ? ? < x ? ? + ?)
P(? ? 2? < x ? ? + 2?)
P(? ? 3? < x ? ? + 3?)
(b) Use the Empirical Rule, to estimate P(?11.648 < x ? 13.474) when x has a normal probability density function with ? = 5.1 and ? = 8.374. (Round your answer to three decimal places.)
(c) Use the normal probability density function to calculate the probability in part (b). (Round your answer to three decimal places.)
Explanation / Answer
a) P(3.274<x<13.474) = 68%
P(-1.826<x<18.574) = 95%
P(-6.926<x<23.674) =99.7%
b)