Answer:
a) Approximately 99.7% of women in this group have platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4.
b) Approximately 68% of women in this group have platelet counts between 201.6 and 328.0.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed(bell shaped) random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 264.8
Standard deviation = 63.2
a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4?
By the Empirical Rule,
Approximately 99.7% of women in this group have platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4.
b. What is the approximate percentage of women with platelet counts between 201.6 and 328.0?
201.6 = 264.8 - 63.2
201.6 is one standard deviation below the mean
328 = 264.8 + 63.2
328 is one standard deviation above the mean
By the Empirical rule,
Approximately 68% of women in this group have platelet counts between 201.6 and 328.0.
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