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A company that produces LED TVs regularly conducts quality checks by taking a random sample of 10 TVs at specified intervals. The historic failure rate of the TVs is 4% and the company wants to ensure the failure rate is maintained at that level by performing these checks.
a. What is the probability that the sample taken will have no defective TVs?
b. What is the probability that the sample will have exactly 1 defective TV?
c. What is the probability that the sample will have 2 or fewer defective TVs?
d. What is the probability that the sample will have 3 or more defective TVs?
e. If there is evidence from the sample that the historic failure rate has gone above the historic value of 4%, the process must be stopped and the situation corrected. Therefore, the value of the maximum number of allowed defective TVs in the sample must be determined. This is done by determining the point at which the number of defective TVs in the sample has risen to where this value has a probability of occurring less than 5% of the time. Based on this criteria, what standard would you set for this process?
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