Question Help The blood platelet counts of a group of women have a bell-shaped d

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The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 249.5249.5 and a standard deviation of 61.361.3. (All units are 1000 cells/muL.) Using the empirical rule, find each approximate percentage below.
a.
What is the approximate percentage of women with platelet counts within 33 standard deviationsdeviations of the mean, or between 65.665.6 and 433.4433.4?
b.
What is the approximate percentage of women with platelet counts between 188.2188.2 and 310.8310.8?

Explanation / Answer

A) P(65.6 < X < 433.4) = P((65.6 - mean)/sd < (X - mean)/sd < (433.4 - mean)/sd)

                                     = P((65.6 - 249.5)/61.3 < Z < (433.4 - 249.5)/61.3)

                                     = P(-3 < Z < 3)

                                     = P(Z < 3) - P(Z < -3)

                                     = 0.9987 - 0.0013

                                     = 0.9974 = 99.74%

b) P(188.2 < X < 310.8) = P((188.2 - mean)/sd < (X - mean)/sd < (310.8 - mean)/sd)

                                      = P((188.2 - 249.5)/61.3 < Z < (310.8 - 249.5)/61.3)

                                      = P(-1 < Z < 1)

                                      = P(Z < 1) - P(Z < -1)

                                      = 0.8413 - 0.1587

                                      = 0.6826 = 68.26%

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