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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.)

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Answer:

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%

Step-by-step explanation:

Mean : [tex]\mu = 246.9[/tex]

Standard deviation : [tex]\sigma = 0.49[/tex]

Empirical rule :

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

This means 68% of data lies between: [tex]\mu-\sigma[/tex]to [tex]\mu+\sigma[/tex]

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

This means 95% of data lies between: [tex]\mu-2\sigma[/tex] to[tex]\mu+2\sigma[/tex]

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

This means 99.7% of data lies between: [tex]\mu-3\sigma[/tex] to[tex]\mu+3\sigma[/tex]

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: [tex]\mu-\sigma[/tex]to [tex]\mu+\sigma[/tex]

[tex]246.9-69.3[/tex]to [tex]246.9+69.3[/tex]

[tex]177.6[/tex]to [tex]316.2[/tex]

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: [tex]\mu-3\sigma[/tex] to[tex]\mu+3\sigma[/tex]

[tex]\mu-3\sigma[/tex] to[tex]\mu+3\sigma[/tex]

[tex]39[/tex]to [tex]454.8[/tex]

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