Question: (i) The gross weekly sale at a certain restaurant is a normal random variable with mean $2200 and standard deviation of $230. What is the probability that weekly sales exceed $2000 in at least 2 of the next 3 weeks?

(ii) A production process operates with 2% nonconforming output. Every hour a sample of 50 units of product is taken, and the number of nonconforming units counted. If one or more nonconforming units are found, the process is stopped and the quality control technician must search for the cause of nonconforming production. Evaluate the probability of stopping the process.

(iii) Suppose nonconforming parts are produced with a rate λ = 8 / hour (i.e. on average, 8 non-conforming parts will be made during a production period of one hour).

1. If X denotes the number of nonconforming parts made during one hour, what distribution does x follow? Please define the parameter(s) needed for defining the distribution based on the information provided.
2. What are the expected value and standard deviation of the number of nonconforming part produced during a 90-min period?
3. What is the probability that at most 20 nonconforming parts produced during a 2.5-hour period?

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