A textile manufacturing process finds that on average, 5 flaws occur per every 2

Question

A textile manufacturing process finds that on average, 5 flaws occur per every 250 yards of material produced.

a) What is the probability of exactly 6 flaws in a 250 yard piece of material? (round your intermediate calculations and final answers to 4 decimal places.)

b) What is the probability of no more than 2 flaws in a 250 yard piece of material? (round your intermediate calculations and final answers to 4 decimal places.)

c) What is the probability of no flaws in a 100 yard piece of material? (Round your intermediate calcualtions and final answers to 4 decimal places.)

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 = 6 ) = ( 250 6 ) * ( 0.02^6) * ( 1 - 0.02 )^244
= 0.1477

b.
P( X < = 2) = P(X=2) + P(X=1) + P(X=0)
= ( 250 2 ) * 0.02^2 * ( 1- 0.02 ) ^248 + ( 250 1 ) * 0.02^1 * ( 1- 0.02 ) ^249 + ( 250 0 ) * 0.02^0 * ( 1- 0.02 ) ^250
= 0.1221

c.
P( X = 0 ) = ( 100 0 ) * ( 0.02^0) * ( 1 - 0.02 )^100
= 0.1326

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