Question

The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 246.9 and a standard deviation of 69.3 (All units are 1000 cells/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 177.6 and 316 2? b. What is the approximate percentage of women with platelet counts between 39.0 and 454.8? a. Approximately % of women in this group have platelet counts within 1 standard deviation of the moan, or between 177.6 and 316.2. (Type an integer or a decimal. Do not round.)

Answer 1

The approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 177.6 and 316.2 is 68%.

The approximate percentage of women with platelet counts between 39.0 and 454.8 is 99.7%

Explanation:

Mean :
`\mu = 246.9`

Standard deviation :
`\sigma = 0.49`

Empirical rule :

1 ) 68% of the data lies within 1 standard deviation of mean

This means 68% of data lies between:
`\mu-\sigma`to
`\mu+\sigma`

2) 95% of the data lies within 2 standard deviation of mean

This means 95% of data lies between:
`\mu-2\sigma` to
`\mu+2\sigma`

3) 99.7% of the data lies within 3 standard deviation of mean

This means 99.7% of data lies between:
`\mu-3\sigma` to
`\mu+3\sigma`

Now to find the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 177.6 and 316. 2

Use rule 1:
`\mu-\sigma`to
`\mu+\sigma`

`246.9-69.3`to
`246.9+69.3`

`177.6`to
`316.2`

So, according to rule 1, 68% of the data lies within 1 standard deviation of mean i.e. 68% of the data lies between 177.6 and 316.2.

Now to find the approximate percentage of women with platelet counts between 39.0 and 454.8?

Use rule 3:
`\mu-3\sigma` to
`\mu+3\sigma`

`\mu-3\sigma` to
`\mu+3\sigma`

`39`to
`454.8`

So, According to rule 3 : 99.7% of the data lies within 3 standard deviation of mean i.e. 99.7% of data lies between 39.0 and 454.8