Mathematics: The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 248.5 and a standard deviation of 61.1. (all units are 1000 cells/mul.) using the empirical rule, find each approximate percentage below. a. what is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 126.3 and 370.7? b. what is the approximate percentage of women with platelet counts between 65.2 and 431.8?

The blood platelet counts of a group of women

Ответ:

1991987

15.03.2022

The blood platelet count is an illustration of normal distribution

Approximately 95% of the data lies within 2 standard deviations of the mean.There are approximately 99.7% of women with platelet count between 65.2 and 431.8

The given parameters are:

$\mathbf{\mu = 248.5}$

$\mathbf{\sigma = 61.1}$

(a) The percentage within 2 standard deviation of mean or between 126.3 and 370.7

Start by calculating the z-score, when x = 126.3 and x = 370.7

$\mathbf{z = \frac{x - \mu}{\sigma}}$

So, we have:

$\mathbf{z = \frac{126.3 -248.5}{61.1}}$

$\mathbf{z = \frac{-122.2}{61.1}}$

$\mathbf{z = -2}$

Also:

$\mathbf{z = \frac{370.7 -248.5}{61.1}}$

$\mathbf{z = \frac{122.2}{61.1}}$

$\mathbf{z = 2}$

The empirical rule states that:

Approximately 95% of the data lies within 2 standard deviations of the mean.

Hence, there are approximately 95% of women with platelet count within 2 standard deviations of the mean.

(b) The percentage with platelet count between 65.2 and 431.8

Start by calculating the z-score, when x = 65.2 and x = 431.8

$\mathbf{z = \frac{x - \mu}{\sigma}}$

So, we have:

$\mathbf{z = \frac{65.2 -248.5}{61.1}}$

$\mathbf{z = \frac{-183.3}{61.1}}$

$\mathbf{z = -3}$

Also:

$\mathbf{z = \frac{431.8 -248.5}{61.1}}$

$\mathbf{z = \frac{183.3}{61.1}}$

$\mathbf{z = 3}$

The empirical rule states that:

Approximately 99.7% of the data lies within 3 standard deviations of the mean.

Hence, there are approximately 99.7% of women with platelet count between 65.2 and 431.8

Read more about normal distributions at:

link

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Ответ:

tedrayoung1

15.03.2022

Mathematics

a. Approximately 95% women have platelet counts between 126.3 and 370.7.

b. Approximately 99.7% women have platelet counts between 65.2 and 431.8.

Step-by-step explanation:

We have been given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 248.5 and a standard deviation of 61.1.

a. Empirical rule of normal distribution states:

$\approx68\%$ of the data lies within 1 standard deviation of the mean