Grueling Stat problem, WHAT AM I DOING WRONG?!!?!?!?!

[StimpackAddict]

I am in no way shape or form asking someone to do my homework, I have already attempted the problem numerous times.
Here is the problem:

2% of hair dryers produced in a certain plant are defective. Estimate the probablility that of 10,000 randomly selected hair dryers, exactly 225 are defective.

Answers: A) 0.0034 B) 0.0057 C) 0.0065 D) 0.0051

Now in order to solve this, You need to find out what the Mean (MU) is, and what the Variance is (sigma)

Q (chance of defective/failure) is = to .02,

because 1-P = Q, and P = .98 (given)

Mean (Mu) = NxP = (225)(.98)= 220.5

Variance (sigma) = Sq rt. of( (n)(p)(q) ) = sq rt of( (10,000) (.98) (.02) ) = 14

Therfore, p=.98 q=.02 Mu=220.5 and Variance=14

Now you must find the Z scores for the sample size of 225, and because it asks for EXACTLY 225 that are defective, you must take .5 from the number for each Z equation.

Therfore:

Z(1) = Avg Mean - Mu / Variance = 224.5 - 220.5 / 14 = .29 (rounded)

Z(2) = Avg Mean - Mu / Variance = 225.5 - 220.5 / 14 = .36 (rounded)

On my Z Score chart, Z(1)'s score of .29 is = to .6141

and Z(2)'s score of .36 is = to .6406

because .29 < Z < .36 ,

you do this operation: .6406 - .6141

but the problem is, I get the answer .0265, which is no where close to the correct answer, which is .0057

I have triple checked my math, and tried it without rounding even, and I still can't get the answer. What the hell am I doing wrong? I even paralleled this problem to an example problem the teacher did in class.

Any input is appreciated. Thanks.

[Siegmund]

2% are defective, it says. Mean is 10000*0.02.

[StimpackAddict]

But doesn't the 2% have to be Q? because if 2% are defective that means 98% are Effective, and the formula for Mean is N x P. Is my mistake that I labeled the 225 defective as "N"?

[StimpackAddict]

Ok, I figured out my problem, thanks anyways.

[1huskerfan]

C(10000, 225)*(.02)^225*(.98)^9775?