MATH 2300 – Sample Final Exam – Summer 2005
Show all the details leading to the solution of a problem, and explain your answers. Use enough significant
decimal digits so that you get a precise answer. All problems are weighted equally.
1. Consider the following data:
11 20 62 61 7
4 5 25 24 32
12 21 2 2 34
31 45 55 56 44
11 11 12 33 35
3 4 14 24 54
(a) Construct a stem-and-leaf diagram of the above data. Using the plot, find the median, the quartiles,
the interquartile range, and the range of the data.
(b) Construct a histogram of the above data.
2. A data set consists of the following observations:
−2,3,3,−2,−4,−9,9,9,−2,2.
(a) Find the sample standard deviation.
(b) Find the sample median, the first quartile, and the third quartile.
(c) Find the sample range and the sample interquartile range.
(d) Construct a boxplot of the above data.
3. Suppose that a student’s math score Xfrom next year’s Graduate Record Exam can be considered as an
observation from a normal population having mean 467 and standard deviation 110. Find the probability
that the student scores are between 290 and 500. Show all work and use the appropriate notation.
4. Suppose Aand Bare events such that P(A) = .4 and P(B) = .25.
(a) Determine P(A∪B) if Aand Bare independent.
(b) Determine P(A∪B) if Aand Bare mutually exclusive.
5. Each year, an insurance company reviews its claim experience in order to set failure rates. Regarding
their damage-only automobile insurance policies, at least one claim was made on 2,073 of the 12,299 policies
in effect for the year. Treating these data as a random sample from the population of all possible damage-
only policies that could be issued, estimate the population proportion of at least one claim and give an 88%
confidence interval for this proportion. Use the proper notation, and show all work.
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