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Answer:
The approximate percentage of women with platelet counts within 3 standard deviations of the mean is 99.7%.
Step-by-step explanation:
We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 247.3 and a standard deviation of 60.7.
Let X = <em>t</em><u><em>he blood platelet counts of a group of women</em></u>
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = population mean = 247.3
= standard deviation = 60.7
Now, according to the empirical rule;
- 68% of the data values lie within one standard deviation of the mean.
- 95% of the data values lie within two standard deviations of the mean.
- 99.7% of the data values lie within three standard deviations of the mean.
Since it is stated that we have to calculate the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 65.2 and 429.4, i.e;
z-score for 65.2 =
= = -3
z-score for 429.4 =
= = 3
So, it means that the approximate percentage of women with platelet counts within 3 standard deviations of the mean is 99.7%.