Question

A textile manufacturing process finds that on average, three flaws occur per every 180 yards of material produced.

a. What is the probability of exactly one flaws in a 180-yard piece of material? (Round your answer to 4 decimal places.)

b. What is the probability of no more than two flaws in a 180-yard piece of material? (Round your answer to 4 decimal places.)

c. What is the probability of no flaws in a 72-yard piece of material? (Round your answer to 4 decimal places.)

Answer 1

X ~ Poisson ( )

Where = 3 flaws per 180 yards.

Poisson probability distribution is

P(X) = e^- * ^X / X!

a)

P(X = 1) = e^-3 * 3¹

= 0.1494

b)

P( X <= 2) = P( X = 0) + P (X = 1) + P (X = 2)

= e^-3 * 3⁰ / 0! + e^-3 * 3¹ / 1! + e^-3 * 3² / 2!

= 0.4232

c)

For 72 yards, = 72/180 * 3 = 1.2

P( X = 0) = e^-1.2 * 1.2⁰

= 0.3012