Production records indicate that 2.2% of the light bulbs produced in a facility

Question

Production records indicate that 2.2% of the light bulbs produced in a facility are defective. A random sample of 30 light bulbs was selected. a. Use the binomial distribution to determine the probability that fewer than three defective bulbs are found. b. Use the Poisson approximation to the binomial distribution to determine the probability that fewer than three defective bulbs are found. c. How do these two probabilities compare? a.The probability is Round to four decimal places as needed.) b. The probability is © (Round to four decimal places as needed.) c. How do these two probabilities compare? O A. The two probabilities have almost the same value. O B. The two probabilities are exactly the same. ° C. The two probabilities differ greatly. O D. The two probabilities cannot be compared Click to select your answerls).

Explanation / Answer

Q.1 Here Pr(Defective) = 2.2% = 0.022

Sample size = 30

(a) If we use binomial distribution n = 30 and p = 0.022

Pr(X <3) = BIN (X < 3, 30, 0.022) = Pr(X=0) + Pr(X =1) + Pr(X =2)

= 30C0 (0.022)0 (0.978)30 +  30C1 (0.022)1 (0.978)29 +  30C2 (0.022)2 (0.978)28

= 0.9722

(b) If we use Poisson distribution

Expected number of defects = 30 * 0.022 = 0.66

Pr(X< 3) = POISSON(X <3 ; 0.66) = 0.9705

(c) Option A is correct as the probabilities are almost the same value.

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