1A.Experience has shown that 1/200 of all CDs produced by a certain machine are

Question

1A.Experience has shown that 1/200 of all CDs produced by a certain machine are defective. If a quality control technician randomly tests twenty CDs, find the probability that at least 2 are defective.

1B. Experience has shown that 1/200 of all CDs produced by a certain machine are defective. If a quality control technician randomly tests twenty CDs and finds at least 2 defective CDs, would the quality control technician think there is something wrong? Why or why not?

1C. Experience has shown that 1/200 of all CDs produced by a certain machine are defective. If a quality control technician randomly tests twenty CDs, find the mean and standard deviation.

Explanation / Answer

Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
a.
P( X < 2) = P(X=1) + P(X=0)
= ( 20 1 ) * 0.005^1 * ( 1- 0.005 ) ^19 + ( 20 0 ) * 0.005^0 * ( 1- 0.005 ) ^20
= 0.9955
P( X > = 2 ) = 1 - P( X < 2) = 0.0045
b.
it is very unlikey event as the result is less than 0.05
c.
Mean ( np ) =20 * 0.005 = 0.1
Standard Deviation ( npq )= 20*0.005*0.995 = 0.3154

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