Question

The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean of 253.2 and a standard deviation of 69.9 ​(All units are 1000 cells/mu​L.) Using the empirical​ rule, find each approximate percentage below.

What is the approximate percentage of women with platelet counts within 1 standard deviation of the​ mean, or between 183.3 and 323.1?

What is the approximate percentage of women with platelet counts between 43.5 and 462.9​?

a. Approximately nothing % of women in this group have platelet counts within 1 standard deviation of the​ mean, or between 183.3 and 323.1 ​(Type an integer or a decimal. Do not​ round.)

b. Approximately nothing % of women in this group have platelet counts between 43.5 and 462.9 ​(Type an integer or a decimal. Do not​ round.)

Answer 1

a)

According to empirical (68 - 95 - 99.7) rule,

Approximately, 68% of the data lies in the 1 standard deviation of the mean.

b)

43.5 = 253.2 - 3 * 69.9

That is 43.5 is 3 standard deviation below the mean.

462.9 = 253.2 + 3 * 69.9

That is 462.9 is 3 standard deviation above the mean.

So,

43.5 and 462.9 are 3 standard deviation of the mean.

According to empirical rule,

Approximately, 99.7% data falls in 3 standard deviation of the mean that is between 43.5 and 462.9