Quick question with probability
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Quick question with probability

[From: ] [author: ] [Date: 12-03-11] [Hit: ]
.. estimate the probability that of 10,000 randomly selected hair dryers, exactly 225 are defective?A)0.......
two percent of hair dryers produced in a certain plant are defective... estimate the probability that of 10,000 randomly selected hair dryers, exactly 225 are defective?
A) 0.0057
B) 0.0051
C) 0.0065
D) 0.0034
D) 0.0367

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i doubt whether you can easily find a binomial calculator that can handle this.
moreover, as #s are very large, & both np & nq are well above 10, the normal approximation will give sufficiently accurate results.

a. µ = np = 10,000*.02
b. σ = sqrt(npq) = sqrt(10,000*.02*.98)
c. with continuity correction, exactly 225 becomes 224.5 to 225.5
d. z1 = (224.5-µ)/σ , z2 = (225.5-µ)/σ
e. P(x = 225) = P(z1 ≤ z ≤ z2) = 0.0057 [A] <------

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10000C225 (.02)^225 (.98)^9775

= you calculate
1
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