Respuesta :
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
