Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. According
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Answer:
A) Approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3 = 95%
B) approximate percentage of women with platelet counts between 53.8 and 442.0 = 99.7%
Step-by-step explanation:
We are given;
mean;μ = 247.9
standard deviation;σ = 64.7
A) We want to find the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3.
Now, from the image attached, we can see that from the empirical curve, the probability of 1 standard deviation from the mean is (34% + 34%) = 68 %.
While probability of 2 standard deviations from the mean is (13.5% + 34% + 34% + 13.5%) = 95%
Thus, approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3 = 95%
B) Now, we want to find the approximate percentage of women with platelet counts between 53.8 and 442.0.
53.8 and 442.0 represents 3 standard deviations from the mean.
Let's confirm 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
Again from the empirical curve attached, we cans that at 3 standard deviations from the mean, we have a percentage probability of;
(2.35% + 13.5% + 34% + 34% + 13.5% + 2.35%) = 99.7%
