Question

20% of all CDs manufactured by an electronics company are defective. A quality control inspector randomly selects 6 CDs from the production line. Use binomial distribution, what is the probability that more than 2 but less than 6 are defectives.

Answer 1

20% CDs are defective      
p = 0.20       …Probability of randomly selecting a defective CD
n = 6       …Sample size of CDs
Let X be the number of defectives in the 6 CDs selected      
Thus, X ~ Binomial distribution with n = 6 and p = 0.2      
       X = 0, 1, 2, 3, 4, 5, 6
To find P(more than 2 but less than 6 are defectives)      
that is to find P(2 < X < 6)      
P(2 < X < 6) = P(X ≤ 5) - P(X ≤ 2)      
   We use Excel function BINOM.DIST to find the probability  
P(2 < X < 6) = BINOM.DIST(5, 6, 0.2, TRUE) - BINOM.DIST(2, 6, 0.2, TRUE)      
   = 0.99994 - 0.90112  
   = 0.0988  
P(more than 2 but less than 6 are defectives) = 0.0988      

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