Week 1 Assignment: Introduction to the Empirical Rule and Chebyshev’s Theorem
Question
A random sample of adult female reaction times has a sample mean of x¯=394.3 milliseconds and sample standard deviation of s=84.6 milliseconds. Use the Empirical Rule to determine the approximate percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds.
Round your answer to the nearest tenth.
Question
A 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.
Question
Suppose 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=2.9 standard deviations of the mean?
Round your answer to the nearest whole number (percent).
Question
Patients 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. Enter the bounds in ascending order.
Question
Toyotas 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. Enter the bounds in ascending order.
Question
At 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. Enter the bounds in ascending order.
Question
A 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.
Question
A random sample of vehicle mileage expectancies has a sample mean of x¯=169,200 miles and sample standard deviation of s=19,400 miles. Use the Empirical Rule to estimate the percentage of vehicle mileage expectancies that are more than 188,600 miles.
Round your answer to the nearest whole number (percent).
Solution
Question
A random sample of adult female reaction times has a sample mean of x¯=394.3 milliseconds and sample standard deviation of s=84.6 milliseconds. Use the Empirical Rule to determine the approximate percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds.
Round your answer to the nearest tenth.
Answer: 99.7%…………….please follow the link below to purchase the solution at $5
