Question

The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 253.1 and a standarddeviation of 84. 3. (All units are 1000 cells/pL.) Using the empirical rule, find each approximate percentage below.• What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, orbetween 124.5 and 381.77b. What is the approximate percentage of women with platelet counts between 188.8 and 317.47

Answer 1

Here is the empirical rule in a bell-shaped distribution.

a. For question a, we need to know the percentage of women with platelet counts within 2 standard deviations. As we can see from the distribution above, the given values would be 95% within 2 standard deviations.

b. Next, we need to know the approximate percentage of women with platelet counts between 188.8 and 317.47. Since it is not stated whether it is between one standard deviation or three standard deviations (since we already know the value of 2 standard deviations), we just need to try and solve to see where it falls.

First, let's try 1 standard deviation:

`\begin{gathered} \mu-\sigma=253.1-64.3=188.8 \\ \mu+\sigma=253.1+64.3=317.4 \end{gathered}`

Here, we can already see that it falls within 1 standard deviation. Therefore, the approximate percentage according to the empirical rule would be 68%