Question

The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean of 256.3 and a standard deviation of 66.8. ​(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 3 standard deviations of the​ mean, or between 55.9 and 456.7​? b. What is the approximate percentage of women with platelet counts between 122.7 and 389.9​?

Answer 1

a) In the interval ( 55,9 ; 456,7 ) we will find 99,7 % of all values

b) In the interval ( 122,7 ; 389,9 ) we find 95,4 % of all values

Explanation:

For a Normal distribution N (μ ; σ ) the Empirical rule establishes that the intervals:

( μ ± σ ) contains 68,3 % of all values

( μ ± 2σ ) contains 95,4 % of all values

( μ ± 3σ ) contains 99,7 % of all values

If N ( 256,3 ; 66,8 )

σ = 66,8 ⇒ 3*σ = 3 * 66,8 = 200,4

Then: 256,3 - 200,4 = 55,9

And 256,3 + 200,4 = 456,7

a) In the interval ( 55,9 ; 456,7 ) we will find 99,7 % of all values

b) 2*σ = 2 * 66,8 = 133,6

Then 256,3 - 133,6 = 122,7

And 256,3 + 133,6 = 389,90

Then in the interval ( 122,7 ; 389,9 ) we find 95,4 % of all values