Question

The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean of 246.3 and a standard deviation of 60.3. ​(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 3 standard deviations of the​ mean, or between 65.4 and 427.2​? b. What is the approximate percentage of women with platelet counts between 125.7 and 366.9​?

Answer 1

Solution:

Given:  The blood platelet counts of a group of women have a​bell-shaped distribution with a mean of 246.3 and a standard deviation of 60.3.

Thus we have: Mean = and standard deviation =

We have to use the empirical​ rule to find approximate percentage.

Part a) Find  the approximate percentage of women with platelet counts within 3 standard deviations of the​ mean, or between 65.4 and 427.2​

Empirical rule:

1) 68% of the data falls within 1 standard deviation from mean

2) 95% of the data falls within 2 standard deviation from mean

3) 99.7% of the data falls within 3 standard deviation from mean

Thus according to empirical rule , we have: 99.7% of the data falls within 3 standard deviation from mean

Thus 99.7% of women with platelet counts within 3 standard deviations of the​ mean, or between 65.4 and 427.2.

Part b) Find the approximate percentage of women with platelet counts between 125.7 and 366.9​.

Find k = Number of standard deviations from mean value.

that is:

Thus platelet counts between 125.7 and 366.9 are 2 standard deviation from mean value.

Thus according to empirical rule , we have: 95% of the data falls within 2 standard deviation from mean

Thus 95% of women with platelet counts between 125.7 and 366.9