Download Please Show Work, when possible! (If you don`t, I can`t give you

Statistics & Probability
Exam #1 (Chapters 1 - 6)
Please Show Work, when possible! (If you don't, I can't give you partial credit!)
1. We collect data from 50 male students about their eye color, hours of homework they did last week,
number of cigarettes they smoke daily and their student id number.
a) Which variable is categorical? (Please explain, if unsure)
b) Which variable is most likely to be bimodal? (Please explain, if unsure)
c) Which variable is most likely to be Normal? (Please explain, if unsure)
d) Which variable is an identifier? (Please explain, if unsure)
.-
2. For the data whose distribution is shown, answer the following questions:
a) The distribution is skewed to the
b) Is the mean smaller or larger than the median? Explain your answer.
c) Is it better to summarize the data with the mean and standard deviation or median and IQR?
Explain your answer.
3
This is a multiple choice question. Just choose the best answer. Suppose that a Normal model
describes the acidity (pH) of rainwater, and that water tested after last week's storm had a z-score of 1.8.
This means that the acidity of that rain.. . (circle one)
Had a pH of 1.8
, Varied with a standard deviation of 1.t?
c) Had a pH 1.8 standard deviations higher than average rainwater
Male
Female
Total
Cash
Check
ChargeIATM
Total
18
18
36
10
12
22
12
30
40
60
100
42
a) What percent of the men paid cash? (show the ratio you are using)
b) What percent of the females charged or use ATM cards? (show the ratio you are using)
C) What percent of those who wrote checks were females? (show the ratio you are using)
d) If you wanted to show the association between gender and method of payment visually, what
kind of graph would you make? (Just name it, you don't have to make it!)
e) Is there evidence of an association between gender and method of payment? Explain your
answer using words and statistics (and show any calculations somewhere for partial credit).
5. An automobile service shop reported the summary statistics shown for repair bills (in $) for their
customers last month. Show Your Work!
Min
Ql
Median
43
Max
Mean
SD
27
88
132
308
1442
284
140
a) Calculate the IQR for the data.
b) Find the "fences" of the data.
c) Were any of the bills outliers? Explain how you made your decision.
d) After checking out a problem with your car the service manager gives you an estimate of "only
$90". Is he right to imply that your bill will be unusually low? Explain your answer.
e) Is the distribution of repair bill costs at this shop skewed or symmetric? Explain how you can
tell. If it's skewed, say what direction it is skewed to.
6. A manufacturer claims that life spans for their copy machines (in months) can be described by a Normal
model with a mean of 42 and standard deviation of 7. Show your work and draw pictures!
a) Draw and clearly label the model and make sure you show the correct percentages for that rule.
b) What percent of the copiers will last longer than 56 months?
c) Find the IQR of the life spans of the copiers.
d) What percent of the copiers are expected to fail before 36 months?
e) The manufacturer wants to'reduce the 32 month failure rate to only 10%. Assuming the mean
lifespan wills stay the same, what standard deviation must they achieve?
f) Briefly explain what that change in standard deviation means in this context. Be specific.
7. For the following description of data, identify the W's, name the variables, specify for each variable
whether its use indicates it should be treated as categorical or quantitative, and, for any quantitative
variable, identify the units in which it was measured (or note that they were not provided):
Ms. Williamson gave her statistics class a survey on the first day of class this semester.
She asked her students their handedness (right or left), height (in inches) and how
difficult the class would be on a scale of 1-5 (l=easy, 5=hard). Her class is located at
City College's Mission Campus. The data will be used in class to illustrate concepts
from the textbook.
Who:
What:
Where:
When:
How:
Why:
All the variables with classifications (and units if quantitative). Explain any answers you are uncertain
about.