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Material Type: Exam; Class: Statistical Methods I; Subject: MATH Mathematics; University: Tennessee Tech University; Term: Unknown 1992;
Typology: Exams
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MATH 3070: MIDTERM: Data sheet
Description of Data. Fortune magazine publishes a list of the world's billionaires each
year. The 1992 list includes 230 individuals. Their wealth (in billions of dollars) and their
age were reported, and the summary statistics are given as follows:
Figure 1: Billionaires' wealth (in billions dollars)
Figure 2: Billionaires' age
Variable Mean S.D L.Quartile Median U.Quartile
wealth 2.53 2.44 1.3 1.8 2.
age 64.5 12.6 57 66 72
MATH 3070: MIDTERM Answers
Question 1. Answer the following questions regarding the world's billionaires in 1992
(see Data sheet ).
cannot tell whether it is unimodal or bimodal).
an outlier? It is 20 billion dollars, and potentially an outlier.
with the correct value $2.0 billion. Does it change the measurement of center? If so,
which, mean or median, would be affected? It does affect mean, but it does not change
median.
We recommend median.
Find the interquartile range for the billionaires' wealth. IQR =2.85โ1.3=1.
What is the percentage of billionaires whose wealth are more than 1.3 billion dollars?
Describe the shape of distribution for the billionaires' age. Unimodal and symmetric.
What percentage of billionaires are between 50 and 60 years old? 0.02ร 10 =0.2 or
does or does not. Since the age distribution is symmetric and unimodal, the empirical
rule does apply.
According to the empirical rule, the interval (52, 77)
approximately covers 68%.
Question 2. Consider a jury decision in which it takes 5 of the seven jurors to convict.
We assume that jurors act independently and each makes the right decision with
probability 0.65. The outcome is identified with the number of the jurors who will make
the right decision , and has the following binomial distribution.
happen (and harder to achieve)? The New River Bridge has
Thus, the Old River Bridge sustains a damage less likely at or above the amount of
430 tons. (The Old River Bridge must have sustained a damage at a lower amount of
weight.)
Question 4. The annual yield of various investment options has a normal distribution
with mean 5% and standard deviation 5%, and are assumed to be independent.
yield is less than 7%? Z =๎ 7 โ 5 ๎/ 5 =0.4 Thus, the probability is
yield of them at the end of term. Find the standard deviation for the average annual
yield. 5 /
Thus, the probability is 0.5๎0.4452=0.
Question 5. An engineer tested 64 tires for highway driving, and obtained the sample
mean 41,300 miles, and the standard deviation 8,800 for the lifetime of the tires.
(a)
(b)
(c)
(d)
(e)
๎ 41300 โ z
64 ๎ , 41300 ๎ z
mean lifetime of tires.
๎ 41300 โ z
64 ๎ , 41300 ๎ z
