Question

The table lists the number of defective 60-watt lightbulbs found in samples of 100 bulbs selected over 25 days from a manufacturing process. Assume that during this time the manufacturing process was not producing an excessively large fraction of defectives. Day 1 2 3 4 5 6 7 8 9 10 Defectives 5 3 5 8 4 5 4 6 6 2 Day 11 12 13 14 15 16 17 18 19 20 Defectives 3 5 4 4 1 2 3 2 4 0 Day 21 22 23 24 25 Defectives 2 2 3 5 4 A hardware store chain purchases large shipments of lightbulbs from the manufacturer described above and specifies that each shipment must contain no more than 4% defectives. When the manufacturing process is in control, what is the probability that the hardware store's specifications are met? (Round your answer to four decimal places.)

Answer 1

Solution :

The mean proportion of defective bulbs over 25 days is 3.56 per 100 bulbs. Let, p = 3.56%

The standard deviation of proportion of defective bulbs over 25 days is,

Sq√p(1-p)/n

=√0.0356(1-0.0356)/25

= 0.0371

We know that the sampling distribution of proportions follow a normal distribution. So the proportion of defective bulbs follow normal distribution with mean = 0.0356 and standard deviation = 0.0371

Probability that hardware store sepcificantion met = Probability that proportion of defective bulbs is less than or equal to 4% = P(p < 0.04)

= P[Z < (0.04 - 0.0356)/0.0371] = P(Z < 0.1186)

= 0.5472

So, the probability that hardware store sepcificantion met is 0.5472

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