The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 264.8 and a standard deviation of 63.2. (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 3 standard deviations of the mean, or between 75.2 and 454.4 ? b. What is the approximate percentage of women with platelet counts between 201.6 and 328.0 ? a. Approximately nothing % of women in this group have platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4. (Type an integer or a decimal. Do not round.) b. Approximately nothing % of women in this group have platelet counts between 201.6 and 328.0. (Type an integer or a decimal. Do not round.)

Question

Mathematics

Mullen

3 November, 06:58

The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 264.8 and a standard deviation of 63.2. (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 3 standard deviations of the mean, or between 75.2 and 454.4 ? b. What is the approximate percentage of women with platelet counts between 201.6 and 328.0 ? a. Approximately nothing % of women in this group have platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4. (Type an integer or a decimal. Do not round.) b. Approximately nothing % of women in this group have platelet counts between 201.6 and 328.0. (Type an integer or a decimal. Do not round.)

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Answers (1)

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Glenn Cruz · Answer 1

a) Approximately 99.7% of women in this group have platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4.

b) Approximately 68% of women in this group have platelet counts between 201.6 and 328.0.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed (bell shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 264.8

Standard deviation = 63.2

a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4 ?

By the Empirical Rule,

Approximately 99.7% of women in this group have platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4.

b. What is the approximate percentage of women with platelet counts between 201.6 and 328.0 ?

201.6 = 264.8 - 63.2

201.6 is one standard deviation below the mean

328 = 264.8 + 63.2

328 is one standard deviation above the mean

By the Empirical rule,

Approximately 68% of women in this group have platelet counts between 201.6 and 328.0.