A process produces strings of Christmas tree lights that historically have exper

Question

A process produces strings of Christmas tree lights that historically have experienced a defective rate of 4%. A customer has placed an order for 150 strings of lights. Use the normal approximation to the binomial distribution to answer the following: Calculate the mean and standard deviation for this distribution. What is the probability that less than 2 strings in this order will be defective? What is the probability that exactly 7 strings in this order will be defective? What is the probability that 3, 4, or 5 strings in this order will be defective? What is the probability that 8, 9, or 10 strings in this order will be defective?

Explanation / Answer

p(defect rate) = .04
n=150

a.

Mean = np = .04*150 = 6.00

Stedv = sqrt(6*96) = 2.4

b.

P(X<2) = P(X=0)+P(X=1) = 0.0159

c.

P(X=7) = 0.14051

d.

P(X=3,4,5)
= P(X=5) - P(X=2)
= 0.4424-0.0584
= .384

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