Question
MATH399 Applied Managerial Statistics
Week 1 Assignment Introduction to the Empirical Rule
and Chebyshev’s Theorem
QuestionAt a carnival, contestants are asked to keep rolling
a pair of dice until they roll snake eyes. The number of
rolls needed has a mean of 36 rolls, with a standard deviation of
5.4 rolls. The distribution of the number of rolls needed is not
assumed to be symmetric.
Between what two numbers of rolls does Chebyshev’s Theorem
guarantee that we will find at least 75% of the contestants?
Round your answers to the nearest tenth.
QuestionA random sample of SAT scores has a sample mean of
x¯=1060 and sample standard deviation of s=195. Use the
Empirical Rule to estimate the approximate percentage of SAT scores
that are less than 865.
Round your answer to the nearest whole number (percent).
QuestionToyotas manufactured in the 1990s have a mean
lifetime of 22.6 years, with a standard deviation of 3.1 years. The
distribution of their lifetimes is not assumed to be symmetric.
Between what two lifetimes does Chebyshev’s Theorem guarantee
that we will find at least 95% of the Toyotas?
Round your answers to the nearest hundredth.
QuestionA random sample of small business stock prices has a
sample mean of x¯=$54.82 and sample standard deviation of
s=$8.95. Use the Empirical Rule to estimate the percentage of
small business stock prices that are more than $81.67.
Round your answer to the nearest hundredth.
QuestionPatients coming to a medical clinic have a mean
weight of 207.6 pounds, with a standard deviation of 22.6 pounds.
The distribution of weights is not assumed to be symmetric.
Between what two weights does Chebyshev’s Theorem guarantees
that we will find at least 95% of the patients?
Round your answers to the nearest tenth.
QuestionSuppose that the distribution of snake lengths in a
certain park is not assumed to be symmetric.
According to Chebyshev’s Theorem, at least what percentage of
snake lengths are within k=2.9standard deviations of the mean?
Round your answer to the nearest whole number (percent).
QuestionA random sample of hybrid vehicle fuel consumptions
has a sample mean of x¯=53.2 mpg and sample standard deviation of
s=4.8 mpg. Use the Empirical Rule to estimate the percentage
of hybrid vehicle fuel consumptions that are less than 43.6 mpg.
Round your answer to the nearest tenth.
QuestionA random sample of lobster tail lengths has a sample
mean of x¯=4.7 inches and sample standard deviation of s=0.4
inches. Use the Empirical Rule to determine the approximate
percentage of lobster tail lengths that lie between 4.3 and 5.1
inches.
Round your answer to the nearest whole number (percent).
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