# 1. Determine whether the following variables are categorical or quantitative. ```1. Determine whether the following variables are categorical or quantitative.
(a) Number of laps a subject can swim
(b) Color of a randomly selected beetle
(c) Birth weight
(d) Hometown
(e) Life of a battery measured in hours
2. The data below represents measurements of the weight of a candy bar in decagrams.
(a) Create a histogram with an appropriate number of intervals which shows
the distributions of this data.
33 30 25 60 63
43 26 35 62 44
45 70 14 33 54
31 33 44 23 47
54 56 43 38 57
64 22 42 13 44
(b) Describe the shape of this data. Is the distribution symmetric? Are there
any outliers?
3. A study is conducted where five colored sticky pads (red, orange, yellow, green,
and purple) are placed in a field and after some time, the insects which have
been trapped on each pad is counted : The results of the study are displayed
in the table below. Create a pie-chart and a bargraph to show the distribution
Red Orange Yellow Green Purple
of this data.
23
45
76
34
10
4. Compute the mean, median, Q1 , Q3 and the standard deviation for the following
observations:4, 5 ,7 , 12 ,5, 8.
5. If the mean of 20 observations is 32, then what is the sum of all of the observations?
6. A student received scores of 92, 83, and 71 on three quizzes. What is the lowest
score that the student can get on the next test, which is out of 200, to achieve
a mean of at least 80?
7. If your scores of the first four exams are 98, 100, 90 and 97, what do you need
to make on the next exam for your overall mean to be at least 90?
8. A student received the following grades on quizzes in a history course: 80, 88,
75, 93, 79, 95, 75, and 96.
Find the mean, and median, and the first and second quartiles of this data.
Also compute the standard deviation.
9. Suppose that the weight of a molar is normal with mean 30mg and standard
deviation 4mg. What portion of molars weigh on average will more than 31mg?
10. To make a knife, a steel blank has to be cut so that it is longer than 7 inches
but shorter than 7.3 inches. Suppose the length of steel blanks which are manufactured follows a normal distribution with mean 7.25 inches and a standard
deviation of 18 of an inch. What portion of the blanks manufactured on average
will meet these specifications?
11. The wingspan of a falcon in feet follows a N(3.3,.1) distribution. What portion
of observations of the wingspan of falcons do you expect to find between 3.1
and 3.5 feet?
12. The wingspan of a falcon in feet follows a N(3.3,.1) distribution. How large
must a bird’s wingspan be in order to place it in the top 10% of all falcons?
13. A circus is recruiting chimpanzees for a show, and they want the chimpanzees
to be either really tall, or really short. The heights of monkeys follow a normal
distribution with mean 4 feet and standard deviation 6 inches. If the circus
purchases a whole barrel of chimps, what portion do you expect to have heights
larger than 5 feet and smaller than 3 feet 7 inches?
14. The data below relates the weights of fruitflys (in micro grams) to the number
Fruit Fly Weight Number of offspring
1
22
43
2
26
47
3
19
40
of offspring they produce.
4
17
38
5
27
50
6
21
42
7
26
46
(a) Create a scatter plot for this data.
(b) Does the data exhibit a positive or negative association?
(c) What is an estimate for the correlation coefficient for this data?
15. Suppose that the heights and shoe sizes are measured of a sample of men from
the University. It is found that the mean height of this sample is 6 feet with a
standard deviation of .5 feet, and that the mean shoe size is a 10 with a standard
deviation of 1. Suppose also that the correlation coefficient is computed between
the two samples and is .75.
(a) Compute the least squares regression line for this data set.
(b) Suppose that Kyle, a university student, wears a size 10.5 shoe. What is
the best prediction for his height?
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