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Stats homework 5

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Question;1. The number of seconds of continuous spray yielded by cans of a brand of outdoor fogger isnormallydistributed with a mean of 260 seconds and a standard deviation of 15 seconds.a) Find the probability a can will yield between 250 and 275 seconds of continuous spray.b) Find the length of time in seconds for which 90% of the cans will exceed in terms ofcontinuousspray time.2. The GRE combined scores for students applying to an engineering school?s Graduate Programarenormally distributed with a mean of 1000 and a standard deviation of 100.a) An applicant needs a minimum score of 1300 to grain admission. What percentage ofapplicantsmeet or exceed the minimum qualification?b) The Director of Admissions wants to change the minimum standard GRE score so that 25% ofapplicants are eligible. What should the new minimum score be?3. A machine fills 100-pound bags with white sand. The actual weight of the sand when themachineoperates at its standard speed of 100 bags per hour follows a normal distribution with a standarddeviation of 1.5 pounds. The mean of the distribution depends on the setting of the machine. Atwhatmean weight should the machine be set so that only 5 percent of the bags are underweight?4. Discretionary household income in a certain state is exponentially distributed with a mean of$4,800per year (i.e.? = 1/4800). Approximately what proportion of households have discretionaryincomegreater than the mean of $4,800 per year?5. The laser used in a Compact Disc player has a time to failure which follows an exponentialdistribution with a mean of 1250 hours of playing time.a) Find the probability that the laser will fail within one year if it is used one hour every day.b) Given that the last has already lasted 2 years, find the probability that it will last a total of 3years.Assume the Compact Disc player is used one hour every day.

 

Paper#62348 | Written in 18-Jul-2015

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