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Answer:
And if we solve for a we got
The highest total cholesterol level a woman in this 20–34 age group can have and still be in the bottom 1% is 91.771 mg per deciliter
Step-by-step explanation:
Let X the random variable that represent the cholesterol level of a population of women between 20-34, and for this case we know the distribution for X is given by:
Where and
We want to find the highest value for the bottom 1% in the distribution, so we need to find a value a who satisfy the following conditions:
(a)
(b)
We can find a z value that satisfy the condition with 0.01 of the area on the left and 0.99 of the area on the right it's z=-2.33. And we can verify that on this case P(Z<-2.33)=0.01 and P(z>-2.33)=0.099
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
The highest total cholesterol level a woman in this 20–34 age group can have and still be in the bottom 1% is 91.771 mg per deciliter