STATISTICS 200 WEEK 4 HOMEWORK PROBLEMS- STAT 200/STAT200 Week 4 Problems

STAT 200/STAT200 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.
The random variable is the waiting time.
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. P(Waiting time = exactly 5) = 0,000

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 .
 =0  =1
a.) The area to the left of z is 15%. -1.04
b.) The area to the right of z is 65%. -0.385
c.) The area to the left of z is 10%. -1.282
d.) The area to the right of z is 5%. 1.645
e.) The area between and z is 95%. 1.96 f.)
z

The area between and z is 99%. 2.576
z

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.
The blood pressure for the people in China.
b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.
.3804
c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.
.7140
d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

, .0841
e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
No, its not because the probability is 38%.
f.) What blood pressure do 90% of all people in China have less than? 157.48 mmHg.
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.
Life of a dishwasher
b.) Find the probability that a dishwasher will last more than 15 years.
.0082
c.) Find the probability that a dishwasher will last less than 6 years.
.0000
d.) Find the probability that a dishwasher will last between 8 and 10 years.
.0541
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?
.0000
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?
9.9 years


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.
Yearly rainfall
b.) Find the probability that the yearly rainfall is less than 100 mm.
.2964
c.) Find the probability that the yearly rainfall is more than 240 mm.
0.0681
d.) Find the probability that the yearly rainfall is between 140 and 250 mm.
.4335
e.) If a year has a rainfall less than 100mm, does that mean it is an unusually dry year? Why or
why not?
.05
f.) What rainfall amount are 90% of all yearly rainfalls more than?
49 mm


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?