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INFORMATION ON THE FIRST MIDTERM EXAMINATION
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SECTION 1 |
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DATE |
September 23, (Wednesday) September 25-29 (online) |
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TIME |
8:00-9:05 |
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PLACE |
SCI. 3610 |
Examination Type: One
sheet of paper (information sheet) is allowed otherwise closed
notes and books
Coverage: Section
1.1 - 2.4 (included), Section 2.3 is not included
The important topics that you
should know for the exam.
| 1. Looking
at Data: Distributions
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| 1.1 Displaying Distributions (excluding Time
Plots)
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Basic definitions: measurement, variable,
frequencies, relative frequencies, distribution of a variable
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Producing and interpreting stemplots and
boxplots
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Shapes of distributions and outliers
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| 1.2 Describing
Distributions
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Finding measures of center (Mean, Median)
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Finding measures of spread or variability (range,
IQR, variance, standard deviation)
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Resistant and nonresistant measures
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Identification of outliers by using 1.5xIQR
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Five-number summary (how to find quartiles)
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Producing and interpreting boxplots
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| 1.3 The Normal
Distributions (excluding Assessing Normality, Quantile and Normal
Plots)
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| Density curve
and its properties
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Normal distribution (N(m,s) and N(0,1))
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Standardized measurements(z-scores)
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(how to find z-scores, use of z-scores,
interpretation of z-scores)
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68-95-99.7 Rule
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Finding proportions (relative frequencies) for
normal distributions
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| Finding a
value given the proportions (relative frequencies)
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| 2. Looking
at Data: Relationships
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| 2.1
Scatterplots
Positive and negative association
Interpretation
2.2 Least Squares Regression
Least squares line, prediction (predict y given
x), interpretation and finding of slope and intercept, finding residuals
2.4 Correlations
Properties and interpretation of correlation r,
and r2
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| 1. Express Courier Service has found that the delivery time for
packages is normally distributed with mean 14 hours and standard
deviation 2 hours. | | a. What percent of
the packages will be delivered in less than 18 hours? | | b. What percent of the packages will be delivered in
more than 16 hours? | c. What percent of
the packages will be delivered in between 13 and 17 hours?
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| 2. The Fight For Life emergency helicopter service is available for
medical emergencies occurring from 15 to 90 miles from the hospital.
Emergencies that occur closer to the hospital can be handled effectively
by ambulance service. A long-term study of the service shows that the
response time from receipt of the dispatch call to arrival at the scene
of the emergency is normally distributed with mean 42 minutes and
standard deviation 8 minutes. For what percent of the receieved calls the
response time will be | | a. Between 30 to
45 minutes? b. Less than 30 minutes? c. More than 60
minutes? | d. How fast a car should go in
order to be in the top 5% fastest cars, in the bottom 5% of the slowest
cars?
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| 3. Scores on the Wechesler Adult Intelligence Scale (a standard
"IQ" test) for people aged 20 to 34 are normally distributed
with mean 110 and standard deviation 25. | | a. Julie only wants to date men in the top 25% on this
intelligence scale. How high must a man score for Julie to date
him? | b. Julie only wants to date men in
the bottom 25% on this intelligence scale. How low must a man score for
Julie to date him?
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4. The life of a certain steel-belted radial tire is normally
distributed with mean 60,000 miles and standard deviation 2,500 miles. In
order to avoid a tire blowout, the company manufactiring the tires will
warn purchasers to replace each tire after it has been used for a given
number of miles. What should be the replacemnet time (in miles) be so
that only 1% of the tires will blow out?
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| 5. Here are the survival times (in days) of lab rats infected with a
deadly bacillus in a test of resistance to infection | | 5.2, 6.3, 4.5, 12.9, 2.2, 4.0, 3.6, 7.1, 3.1, 10.0,
| | 6.2, 4.7, 7.5, 5.7, 1.4, 5.9, 2.6, 4.5, 8.4,
3.4 | | a. Make a stemplot of these data
and interpret | | b. Compute the
mean | | c. Give the five-number summary
for this distribution | | d. Find the
interquartile range (IQR) | | e. Construct
a boxplot and interpret | | f. Use the
1.5xIQR criterion to spot suspected outliers | g. Based on the shape of this distribution, would you be
willing to report the mean and standard deviation as helpful descriptive
measures? Please justify your answer.
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| 6. The following data give the time that 20 students took to
complete a statistics exam. | | 55 49 53 59 38 56
39 58 47 53 | | 58 42 37 43 47 44 55 51 46
45 | | a. Make a stemplot of these data and
interpret b. Compute the mean | | c.
Give the five-number summary for this distribution d. Find the
interquartile range (IQR) | | e. Construct
a boxplot and interpret f. Use the 1.5xIQR criterion to spot
suspected outliers | g. Based on the
shape of this distribution, would you be willing to report the mean and
standard deviation as helpful descriptive measures? Please justify your
answer.
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| 7. It is claimed that the percentage of apples attacked by coddling
moths is greater on trees bearing a small crop of apples. A sample of 12
trees gave data for x (size of crop in hundreds of fruits) and y
(percentage of wormy fruits). The least squares regression line was
y=68.3-0.8x, and the correlation coefficient was r =
-0.85. | | a. Intrepret 68.3 and
.8 | | b. Predict percentage of wormy
fruits if a tree has 12 hundred apples. | | c. one tree in the sample had 12 hundred apples and
61.0% of them wormy. Find the residual for this tree. | d. Interpret r=-0.85 and r2.
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8. Araceli Silva lives in a city in which the average cost of rent
for a one-bedroom apartment is $379 with a standard deviation of $65.
Brenda Kantor lives in a city in which the average cost of rent for a
similar apartment is $469 with a standard deviation of $87. Araceli and
Brenda live in one-bedroom apartments and pay $325 and $410,
respectively. Relatively speaking, which woman has the cheaper rent?
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