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 -z and z is 95%. (Hint draw a picture and figure out the area to the left of the -z.)
f.) The area between -z 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
146.8
383
90.9
178.1
267.5
95.5
156.5
180
90.9
139.7
200.2
171.7
187.2
184.9
70.1
58
84.1
55.6
133.1
271.8
135.9
71.9
99.4
110.6
47.5
97.8
122.7
58.4
154.4
173.7
118.8
88
84.6
171.5
254.3
185.9
137.2
138.9
96.2
85
45.2
74.7
264.9
113.8
133.4
68.1
156.4
6.5.2
A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21.
a.) If you take a sample of size 10, can you say what the shape of the distribution for the sample mean is? Why?
b.) For a sample of size 10, state the mean of the sample mean and the standard deviation of the sample mean.
c.) For a sample of size 10, find the probability that the sample mean is more than 241.
d.) If you take a sample of size 35, can you say what the shape of the distribution of the sample mean is? Why?
e.) For a sample of size 35, state the mean of the sample mean and the standard deviation of the sample mean.
f.) For a sample of size 35, find the probability that the sample mean is more than 241.
g.) Compare your answers in part c and f. Why is one smaller than the other?
6.5.4
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). Blood pressure is normally distributed.
a.) State the random variable.
b.) Suppose a sample of size 15 is taken. State the shape of the distribution of the sample mean.
c.) Suppose a sample of size 15 is taken. State the mean of the sample mean.
d.) Suppose a sample of size 15 is taken. State the standard deviation of the sample mean.
e.) Suppose a sample of size 15 is taken. Find the probability that the sample mean blood pressure is more than 135 mmHg.
f.) Would it be unusual to find a sample mean of 15 people in China of more than 135 mmHg? Why or why not?
g.) If you did find a sample mean for 15 people in China to be more than 135 mmHg, what might you conclude?
6.5.6
The mean cholesterol levels of women age 45-59 in Ghana, Nigeria, and Seychelles is 5.1 mmol/l and the standard deviation is 1.0 mmol/l (Lawes, Hoorn, Law & Rodgers, 2004). Assume that cholesterol levels are normally distributed.
a.) State the random variable.
b.) Find the probability that a woman age 45-59 in Ghana has a cholesterol level above 6.2 mmol/l (considered a high level).
c.) Suppose doctors decide to test the woman’s cholesterol level again and average the two values. Find the probability that this woman’s mean cholesterol level for the two tests is above 6.2 mmol/l.
d.) Suppose doctors being very conservative decide to test the woman’s cholesterol level a third time and average the three values. Find the probability that this woman’s mean cholesterol level for the three tests is above 6.2 mmol/l.
e.) If the sample mean cholesterol level for this woman after three tests is above 6.2 mmol/l, what could you conclude?
6.5.8
A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years (“Appliance life expectancy,” 2013). The life of a dishwasher is normally distributed. Suppose you are a manufacturer and you take a sample of 10 dishwashers that you made.
a.) State the random variable.
b.) Find the mean of the sample mean.
c.) Find the standard deviation of the sample mean.
d.) What is the shape of the sampling distribution of the sample mean? Why?
e.) Find the probability that the sample mean of the dishwashers is less than 6 years.
f.) If you found the sample mean life of the 10 dishwashers to be less than 6 years, would you think that you have a problem with the manufacturing process? Why or why not?
We provide professional writing services to help you score straight A’s by submitting custom written assignments that mirror your guidelines.
Get result-oriented writing and never worry about grades anymore. We follow the highest quality standards to make sure that you get perfect assignments.
Our writers have experience in dealing with papers of every educational level. You can surely rely on the expertise of our qualified professionals.
Your deadline is our threshold for success and we take it very seriously. We make sure you receive your papers before your predefined time.
Someone from our customer support team is always here to respond to your questions. So, hit us up if you have got any ambiguity or concern.
Sit back and relax while we help you out with writing your papers. We have an ultimate policy for keeping your personal and order-related details a secret.
We assure you that your document will be thoroughly checked for plagiarism and grammatical errors as we use highly authentic and licit sources.
Still reluctant about placing an order? Our 100% Moneyback Guarantee backs you up on rare occasions where you aren’t satisfied with the writing.
You don’t have to wait for an update for hours; you can track the progress of your order any time you want. We share the status after each step.
Although you can leverage our expertise for any writing task, we have a knack for creating flawless papers for the following document types.
Although you can leverage our expertise for any writing task, we have a knack for creating flawless papers for the following document types.
From brainstorming your paper's outline to perfecting its grammar, we perform every step carefully to make your paper worthy of A grade.
Hire your preferred writer anytime. Simply specify if you want your preferred expert to write your paper and we’ll make that happen.
Get an elaborate and authentic grammar check report with your work to have the grammar goodness sealed in your document.
You can purchase this feature if you want our writers to sum up your paper in the form of a concise and well-articulated summary.
You don’t have to worry about plagiarism anymore. Get a plagiarism report to certify the uniqueness of your work.
Join us for the best experience while seeking writing assistance in your college life. A good grade is all you need to boost up your academic excellence and we are all about it.
We create perfect papers according to the guidelines.
We seamlessly edit out errors from your papers.
We thoroughly read your final draft to identify errors.
Work with ultimate peace of mind because we ensure that your academic work is our responsibility and your grades are a top concern for us!
Dedication. Quality. Commitment. Punctuality
Here is what we have achieved so far. These numbers are evidence that we go the extra mile to make your college journey successful.
We have the most intuitive and minimalistic process so that you can easily place an order. Just follow a few steps to unlock success.
We understand your guidelines first before delivering any writing service. You can discuss your writing needs and we will have them evaluated by our dedicated team.
We write your papers in a standardized way. We complete your work in such a way that it turns out to be a perfect description of your guidelines.
We promise you excellent grades and academic excellence that you always longed for. Our writers stay in touch with you via email.