Question

The Empirical Rule Based on Data Set 1" Body Data" in appendix B, blood platelet counts of women have a bell shaped distribution with a mean of 255.1 and a standard deviation of 65.4.(All units are 1000 cells/L.) Using the empirical rule: [Sketch the normal curve first] 1. idth ths 2 a. of women with platelet counts are within two standard deviation of the mean? The values are from ( b.- % of women with platelet counts are within one standard deviation of the .. mean? The values are from ( c, % of women with platelet counts are within three standard deviation of the mean? The values from (

Answer 1

Blood platelet counts of women have a bell shaped distribution.

Mean = $\mu$ = 255.1

Standard deviation = $\sigma$ = 65.4

{ Empirical rule :

According to Empirical rule ,

1) 68% of data falls within the first standard deviation from the mean.

In mathematical notation, this is represented as: $\mu \pm \sigma$

2) 95% fall within two standard deviations.

The mathematical notation for this is : $\mu \pm 2*\sigma$

3) 99.7% fall within three standard deviations

The mathematical notation for this is: $\mu \pm 3*\sigma$ }

Normal curve -

a )

95% of women with platelet counts are within two standard deviation of the mean.
The values are ( 124.3 , 385.9 )

b)

68% of women with platelet counts are within one standard deviation of the mean.
The values are ( 189.7 , 320.5 )

c)

99.7% of women with platelet counts are within three standard deviation of the mean.
The values are ( 58.9 , 451.3 )