The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 250.8 and a standard deviation of 69.3. (all units are 1000 cells/muμl.) 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 181.5 and 320.1? b. what is the approximate percentage of women with platelet counts between 112.2 and 389.4?

a) 68%; b) 99.5%

Step-by-step explanation:

The empirical rule states that 68% of data falls within 1 standard deviation of the mean; 95% of data falls within 2 standard deviations of the mean; and 99.7% of data falls within 3 standard deviations of the mean.

For part a,

We are asked the approximate percentage of women whose platelet counts are within 1 standard deviation of the mean.  According to the empirical rule, this is 68%.

For part b,

We are given the endpoints of the interval.  The lower endpoint is 181.5; this is 250.8-181.5 = 138.6 away from the mean.  Dividing by the standard deviation, 69.3, we have

138.6/69.3 = 2

This is 2 standard deviations away from the mean.

The higher endpoint is 320.1; this is 320.1-181.5 = 138.6 away from the mean.  Dividing by the standard deviation, 69.3, we have

138.6/69.3 = 2

This is standard deviations away from the mean.

This means this interval includes about 95% of women.

1. 22

2. 1

3. 7

4. 18

step-by-step explanation

e2020 got it right

this is false ^.^ lol