The blood platelet counts of a group of women have a bell-shaped distribution wi

Question

The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 257.2 and a standard deviation of 67.6 (All units are 1000 cells/ mu L.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 2 standard deviations deviations of the mean, or between 122.0 and 392.4? b. What is the approximate percentage of women with platelet counts between 54.4 and 460.0?

a. Approximately nothing % of women in this group have platelet counts within 2 standard deviations deviations of the mean, or between 122.0 and 392.4 (Type an integer or a decimal. Do not round.)

b. Approximately nothing % of women in this group have platelet counts between 54.4 and 460.0. (Type an integer or a decimal. Do not round.)

Explanation / Answer

a) By the empirical rule,

Approximately 95 % of women in this group have platelet counts within 2 standard deviations deviations of the mean, or between 122.0 and 392.4

b) z score for 54.4 = (54.4 - 257.2)/67.6 = -3

z score for 460 = (460 - 257)/67.6 = 3

Hence,

Approximately 99.7 % of women in this group have platelet counts between 54.4 and 460.0.

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