Quality control engineers at a semiconductor plant monitor microchips for a specific manufacturing defect. Historical data indicates that the probability of a microchip possessing this defect is 0.012.
Define a suitable model for the distribution of the number of microchips possessing this defect in a batch of nnn chips.
State one modeling assumption required for the distribution in part (a) to be valid.
Using a suitable approximation, determine the probability that exactly 5 out of a batch of 250 microchips are found to have this defect.
Justify the use of the approximation chosen in part (c).
A manufacturer claims that 65% of their solar panels exceed an efficiency rating of 22%.
From a random sample of 180 panels, 104 are found to exceed this rating.
Using a suitable approximation, test the manufacturer's claim at the 5% level of significance. State your hypotheses clearly.
