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 6 9 3 4 4 6 6 2

Day 11 12 13 14 15 16 17 18 19 20

Defectives 3 4 3 4 1 3 4 2 5 1

Day 21 22 23 24 25

Defectives 3 3 4 6 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

total number of defectives =98

total sample size =25*100 =2500

proportion of defective =98/2500 =0.0392

sample size       =n=

100

std error of proportion=σp=√(p*(1-p)/n)=

0.0194

probability =P(X<0.04)=(Z<(0.04-0.0392)/0.019)=P(Z<0.0412)=0.5160