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Stats homework 5

Question # 00010434
Subject: Statistics
Due on: 03/31/2014
Posted On: 03/17/2014 05:44 AM

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1. The number of seconds of continuous spray yielded by cans of a brand of outdoor fogger is
normally
distributed 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 of
continuous
spray time.

2. The GRE combined scores for students applying to an engineering school’s Graduate Program
are
normally 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 of
applicants
meet or exceed the minimum qualification?
b) The Director of Admissions wants to change the minimum standard GRE score so that 25% of
applicants 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 the
machine
operates at its standard speed of 100 bags per hour follows a normal distribution with a standard
deviation of 1.5 pounds. The mean of the distribution depends on the setting of the machine. At
what
mean 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
$4,800
per year (i.e. ? = 1/4800). Approximately what proportion of households have discretionary
income
greater 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 exponential
distribution 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 3
years.
Assume the Compact Disc player is used one hour every day.

Tags homework stats mean standard seconds minimum bags probability machine used score hour year player time disc compact distributed laser exceed deviation distribution cans weight continuous follows sand household certain normal state income

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