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BrandiMR
02-25-2010, 01:38 PM
I'm doing a sample test for a Stats quiz I have on Tuesday and I've run into a question that I just cannot get. :confused: I'm sure the method to use is right under my nose, but its driving me crazzzzy. :eek:

HDL cholesterol levels of males aged 20-29 are Normally distributed with a mean of 5.5 and a standard deviation of 1.2 For the nine male employees of a certian company, what is the probability that exactly five of them have HDL cholesterol levels exceeding 5.5?

Since it uses "exactly 5", I went to the binomial distribution and tried to use formulas I know to fill in the various parts of the binomial.

I went like this:

Mu = np
5.5 = 9p
p = 0.611

q would then be:

q = 1-p
q = 1-0.611
q = 0.389

right?

So then:

P[X=5] = (9C5) (0.611)^5 (0.389)^9-5
= 0.2457?

The answer choices I have are:
(A) 0.1056 (B) 0.3203 (C) 0.7539 (D) 0.0667 (E) 0.4364 (F) 0.8944 (G) 0.5636 (H) 0.2461 (I) 0.9333 (J) 0.6797

...and none of them are what I came up with. (H) 0.2461 is close, but I tried again without rounding anything and its still the same answer. =/ One thing I'm worried about is that I didn't use the standard deviation at all. It's mentioned right in the question, so it should be used in the calculation somewhere, shouldn't it? D:

Am I even close to the right direction? :( Any help would be appreciated.

BGM
02-25-2010, 03:16 PM
The "20-29 age" is an irrelevant information.
The value of p is the probability that each of the nine employees has HDL cholesterol
level X exceeding 5.5. Since X is normally distributed with mean 5.5 and the normal
distribution is a symmetric distribution,
so its median = mean = 5.5 and hence Pr{X > 5.5} = 1/2
i.e. p = 1/2
So the required probability = (9C5)(1/2)^5(1/2)^4 = 126/512 = 0.24609375
After rounding up the answer should be H

BrandiMR
02-25-2010, 04:36 PM
D'oh!

I knew it'd be something easy like that.

Thank you so much for your help. :)