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iragen [17]
3 years ago
15

In a randomly selected sample of women ages 20–34, the mean total cholesterol level is 188 milligrams per deciliter with a stand

ard deviation of 41.3 milligrams per deciliter. Assume the total cholesterol levels are normally distributed. Find the highest total cholesterol level a woman in this 20–34 age group can have and still be in the bottom 1%. (Round your answers to two decimal places)
Mathematics
1 answer:
Vinvika [58]3 years ago
5 0

Answer:

z=-2.33

And if we solve for a we got

a=188 -2.33*41.3=91.771

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:

X \sim N(188,41.3)  

Where \mu=188 and \sigma=41.3

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:

P(X>a)=0.99   (a)

P(X   (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:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-2.33

And if we solve for a we got

a=188 -2.33*41.3=91.771

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

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