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?
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.
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?
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.
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?
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?
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.
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.

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