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I want to start this post by apologizing for posting this here as opposed to the math forum, but it is for the reason that the math forum is dead, and replies would take too long, and I need verification within a few minutes. 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. |
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