Problem#l.. In a certain process, the probability of producing an oversize assembly is 0.05.(a) In a sample of 300 randomly chosen assemblies, what is the probability that fewer

than 20 of them are oversize?(b) What is the expected number of oversized assemblies?

Problem#2. Students may choose between a 3-semester-hour course in physicswithout labs and 4-semester-hour course with labs. The final written examination is thesame or each section. If 12 students in the section with labs made an average examinationgrade of 84 with a standard deviation of 4, and 18 students in the section without labsmade an average grade of 77 with a standard deviation of 6, find a 99% confidenceinterval for the difference between the average grades for the two courses. Whatassumptions need to be made in this construction?

Problem#3. A manufacture of a candy must monitor the temperature at which thecandies are baked. Too much variation will cause inconsistency in the taste of the candy.A random sample of 30 batches of candy is selected. And the sample standard deviationof the temperature is 2.1 F.

(a) Set up a 95% confidence interval estimate of the population standard deviation.(b) What assumptions need to be made in (a)?

Problem#4. A random sample of 400 electric components manufactured by a certainprocess are tested, and 30 are found to be defective. Let p represent the proportion ofcomponents manufactured by this process that are defective. Find a 95% confidenceinterval for p.

Problem#5. The amount of time that a drive-through bank teller spends on a customeris a random variable with a mean 3.2 minutes and a standard deviation 1.6 minutes. If arandom sample of 64 customers is observed, find the probability that their mean time atthe teller's counter is

(a) at most 2.7 minutes;(b) more than 3.5 minutes;(c) at least 3.2 minutes but less than 3.4 minutes.

Problem#6. The lifetime of a cooling fan, in hours, that is used in a computer systemhas the Weibull distribution with a= 1.5 and f3 = 10,000.

(a) What is the probability that a fan lasts more than 10,000 hours?(b) What is the probability that a fan lasts less than 5,000 hours?(c) What is the probability that a fan lasts between 3,000 and 9,000 hours?

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