Question

10. Based on the blood platelet counts from the WOMEN PLATELET data set below, women have blood platelet counts that follow a bell-shaped distribution with a mean of 280 and a standard deviation of 65. Using Chebyshev’s Theorem, what is the approximate percentage of women with platelet counts...

a. within two (2) standard deviations of the mean?

b. What are the minimum and maximum blood platelet counts that are within two standard deviations of the mean?

Answer 1

SOLUTION:

From given data,

10. Based on the blood platelet counts from the WOMEN PLATELET data set below, women have blood platelet counts that follow a bell-shaped distribution with a mean of 280 and a standard deviation of 65. Using Chebyshev’s Theorem, what is the approximate percentage of women with platelet counts.

Mean = 280

Standard deviation = 65

From the given information , a bell-shaped distribution is of mean of 280 cells / and a standard deviation of 65 cells / .

a. within two (2) standard deviations of the mean?

By Chebyshev’s Theorem , The population of given set of data lying within 2 standard deviations of the mean is at least 3/4 or 75% . Thus , 75% of Women with platelet counts within 2 standard deviations of the men are

-2s = 280-2(65)

= 150 cells /

and

+2s = 280+2(65)

= 410 cells /

The accompanying normal curve is,

b. What are the minimum and maximum blood platelet counts that are within two standard deviations of the mean?

Therefore , the minimum and maximum platelet counts within 2 standard deviations of the mean are  150 cells / and  410 cells / respectively.