2.) Suppose that the number of requests for assistance receivedby a towing service is a Poisson process with rate a = 6 perhour.
a.) Find the expected value and variance of the number ofrequests in 30 minutes. Then compute the probability that there isat most one request in 30 minute interval.
b.) What is the probability that more than 20 minutes elapsebetween two successive requests? Clearly state the random variableof interest using the context of the problem and what probabilitydistribution it follows.
3.) Certain ammeters are produced under the specification thatits gauge readings are normally distributed with main 1 amp andvariance 0.04 amp^2, respectively.
a.) What is the probability that a gauge reading from the testis more than 1.15 amp?
b.) Find the value of a gauge reading of an ammeter such that20% of ammeters would have higher readings than that. In otherwords, find the 80-th percentile of gauge readings.
4. ) Suppose that a quality control engineer believes that themanufacturing process is flawed and wishes to estimate the truemean gauge reading. The engineer samples 130 of these ammeters andmeasures their gauge readings. From these, the engineer obtains themean and standard deviation of 1.1 amp and 0.18 amp, respectively.Calculate and interpret a 98% confidence interval for the true meangauge reading.
