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The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean of 246.8 and a standard deviation of 67.2. ​(All units are 1000 ​cells/μ​L.) Using the empirical​ rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the​ mean, or between 179.6 and 314.0​? b. What is the approximate percentage of women with platelet counts between 45.2 and 448.4​?

Sagot :

Answer:

a. 68%

b. 99.7%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed 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 = 246.8

Standard deviation = 67.2

a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the​ mean, or between 179.6 and 314.0​?

By the Empirical Rule, approximately 68%.

b. What is the approximate percentage of women with platelet counts between 45.2 and 448.4​?

45.2 = 246.8 - 3*67.2

448.4 = 246.8 + 3*67.2

Within 3 standard deviations of the mean, so approximately 99.7%.

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