Suppose that the hemoglobin levels among healthy females are normally distributed with a mean of 13.9 gdL. Research shows that exactly 95% of healthy females have a hemoglobin level below 16.2 gdL. What is the standard deviation of the distribution of hemoglobin levels in healthy females? Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.gdL CheckSave For LaterSubmit AssignmentTerms of Use
Question
Suppose that the hemoglobin levels among healthy females are normally distributed with a mean of 13.9 gdL. Research shows that exactly 95% of healthy females have a hemoglobin level below 16.2 gdL. What is the standard deviation of the distribution of hemoglobin levels in healthy females? Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.gdL CheckSave For LaterSubmit AssignmentTerms of Use
Solution
To find the standard deviation, we first need to understand that for a normal distribution, 95% of the data falls within 1.96 standard deviations from the mean.
Given that 95% of healthy females have a hemoglobin level below 16.2 gdL, we can set up the following equation:
Mean + 1.96(Standard Deviation) = 16.2 gdL
We know the mean is 13.9 gdL, so we can substitute that into the equation:
13.9 gdL + 1.96(Standard Deviation) = 16.2 gdL
Next, we subtract 13.9 gdL from both sides of the equation to isolate the term with the standard deviation:
1.96(Standard Deviation) = 16.2 gdL - 13.9 gdL
1.96(Standard Deviation) = 2.3 gdL
Finally, we divide both sides of the equation by 1.96 to solve for the standard deviation:
Standard Deviation = 2.3 gdL / 1.96
Standard Deviation = 1.1735 gdL
Rounding to at least two decimal places, the standard deviation of the distribution of hemoglobin levels in healthy females is approximately 1.17 gdL.
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