19 Oct Homework Problems
STAT 200 Week 4 Homework Problems
6.1.2
1.) The commuter trains on the Red Line for the Regional Transit Authority (RTA) in Cleveland, OH, have a waiting time during peak rush hour periods of eight minutes (“2012 annual report,” 2012).
a.) State the random variable.
b.) Find the height of this uniform distribution.
c.) Find the probability of waiting between four and five minutes.
d.) Find the probability of waiting between three and eight minutes.
e.) Find the probability of waiting five minutes exactly.
6.3.2
Find the z-score corresponding to the given area. Remember, z is distributed as the standard normal distribution with mean of and standard deviation .
a.) The area to the left of z is 15%.
b.) The area to the right of z is 65%.
c.) The area to the left of z is 10%.
d.) The area to the right of z is 5%.
e.) The area between and z is 95%. (Hint draw a picture and figure out the area to the left of the .)
f.) The area between and z is 99%.
6.3.4
According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998). Assume that blood pressure is normally distributed.
a.) State the random variable.
b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.
c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.
d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
f.) What blood pressure do 90% of all people in China have less than?
6.3.8
A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years (“Appliance life expectancy,” 2013). Assume the life of a dishwasher is normally distributed.
a.) State the random variable.
b.) Find the probability that a dishwasher will last more than 15 years.
c.) Find the probability that a dishwasher will last less than 6 years.
d.) Find the probability that a dishwasher will last between 8 and 10 years.
e.) If you found a dishwasher that lasted less than 6 years, would you think that you have a problem with the manufacturing process? Why or why not?
f.) A manufacturer of dishwashers only wants to replace free of charge 5% of all dishwashers. How long should the manufacturer make the warranty period?
6.3.10
The mean yearly rainfall in Sydney, Australia, is about 137 mm and the standard deviation is about 69 mm (“Annual maximums of,” 2013). Assume rainfall is normally distributed.
a.) State the random variable.
b.) Find the probability that the yearly rainfall is less than 100 mm.
c.) Find the probability that the yearly rainfall is more than 240 mm.
d.) Find the probability that the yearly rainfall is between 140 and 250 mm.
e.) If a year has a rainfall less than 100mm, does that mean it is an unusually dry year? Why or why not?
f.) What rainfall amount are 90% of all yearly rainfalls more than?
6.4.4
Annual rainfalls for Sydney, Australia are given in table #6.4.6. (“Annual maximums of,” 2013). Can you assume rainfall is normally distributed?
Table #6.4.6: Annual Rainfall in Sydney, Australia
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