Question

The blood platelet counts of a group of women have a? bell-shaped distribution with a mean of 249.9 and a standard deviation of 68.8. ?(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 1 standard deviation of the? mean, or between 181.1 and 318.7?? b. What is the approximate percentage of women with platelet counts between 43.5 and 456.3??

Answer 1

Given,

= 249.9, = 68.8

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

Approximately, 68% data falls in 1 standard devation of the mean.

Approximately, 95% data falls in 2 standard devation of the mean.

Approximately, 99.7% data falls in 3 standard devation of the mean.

a)

We have to calculate (181 < X < 318.7) = ?

OR within 1 standard deviation of the mean = ?

By emperical rule,

(181 < X < 318.7) = 68%

b)

P( 43.5 < X < 456.3) = ?

We can write 456.3 in terms of and as

456.3 = 249.9 + 3 * 68.8

456.3 = + 3 *

That is 456.3 is 3 standard deviation above the mean.

Similarly,

43.5 = 249.9 - 3 * 68.8

43.5 is 3 standard deviation below the mean.

So,

43.5 and 456.3 are 3 standard deviation of the mean.

By emperical rule,

P( 43.5 < X < 456.3) = 99.7%