Answer:
A) The estimated proportion of women whose platelet counts fall within 2 standard deviations of the mean, or between 118.5 and 377.3, is 95%.
B) The estimated percentage of women with platelet counts ranging from 53.8 to 442.0 is 99.7%.
Step-by-step explanation:
Provided data:
mean;μ = 247.9
standard deviation;σ = 64.7
A) We seek to find the estimated percentage of women with platelet counts within 2 standard deviations from the mean, which translates to values between 118.5 and 377.3.
Based on the attached image, the empirical curve indicates that the likelihood within 1 standard deviation of the mean is (34% + 34%) = 68%.
In contrast, the likelihood within 2 standard deviations from the mean is (13.5% + 34% + 34% + 13.5%) = 95%
Therefore, the estimated percentage of women having platelet counts within 2 standard deviations of the mean, or ranging from 118.5 to 377.3, equals 95%
B) Next, we want to determine the estimated percentage of women with platelet counts between 53.8 and 442.0.
The values of 53.8 and 442.0 correspond to 3 standard deviations from the mean.
Let’s verify that.
Since mean;μ = 247.9
standard deviation;σ = 64.7;
μ = 247.9
σ = 64.7
μ + 3σ = 247.9 + 3(64.7) = 442
Also;
μ - 3σ = 247.9 - 3(64.7) = 53.8
From the attached empirical curve, it can be seen that at 3 standard deviations from the mean, the probability percentage is;
(2.35% + 13.5% + 34% + 34% + 13.5% + 2.35%) = 99.7%
