A PC manufacturer buys bulbs from a supplier. The supplier specifies that 5% of

Question

A PC manufacturer buys bulbs from a supplier. The supplier specifies that 5% of the bulbs are compact fluorescent. The manufacturer randomly and independently selects and inspects 4 bulbs from a shipment.

a) what is the probability that two of the selected bulbs are compact fluorescent?
ANSWER MIGHT BE 0.015


b) what is the probability that between one and two selected bulbs are compact fluorescent?
ANSWER MIGHT BE 0.185


c) Suppose that the PC manufacturer receives 8 shipments in a week, and randomly selects and inspects 4 bulbs per shipment. What is the probability that there will be 1 shipment containing two compact fluorescent bulbs?
ANSWER: 0.108

Explanation / Answer

This we can consider as Bionomial Distribution............. Total No.of Bulbs = 4. probability th getting compact fluroscent = p = 0.05 probability that notgetting compact one = q = 1-p = 0.95 a)what is the probability that two of the selected bulbs are compact fluorescent? P(X=2) = 4 C 2 (0.05)^2 * (0.95)^2 = 6*0.05^2 * 0.95^2 = 0.015 Ans. b) what is the probability that between one and two selected bulbs are compact fluorescent? P(x=1) + p(x=2) = 4 C 1 0.05*o.95^3 + 4 C 2 0.05^2 * 0.95^2 = 4*0.05*0.95^3 + 0.015 = 0.185 Ans. c) Now we will use result of a here means we will again consider this as bionomial distribution with N = 8 and probability that two of the selected bulbs are compact fluorescent = p = 0.015 probability that two of the selected bulbs are not compact fluorescent = q = 1- 0.015 = 0.985 Now the probability that there will be 1 shipment containing two compact fluorescent bulbs = 8 C 1* 0.015*0.98567 = 0.108 Ans. Where n c r represents n! / r!*(n-r)!

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