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Chapter 3: Q. 3.97 (page 112)

If the condition for using the empirical rule is met,why should that rule be used insted of Chebyshev's rule.

Short Answer

Expert verified

Chebyshev's rule is a lower bound.

Step by step solution

01

Given information

We have to tell the difference between Chebyshev's and empirical rule.

02

Explanation

Chebyshev's rule is lower bound on the proportion of data which can be found within a certain number of standard deviations from the mean
-if the distribution is rough bell shaped then the empirical rule in general provides a better estimate than chebyshev's rule.

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Most popular questions from this chapter

The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of 60miles per hour (mph) and. according to the online document "Cheetah Conservation in Southern Africa" by J. Urbaniak, the cheetah is capable of speeds up to 72mphThe following table gives the top speeds, in miles per hour, arranged in increasing order, for a sample of 35cheetahs.

The sample mean and sample standard deviation of these speeds are 59.53mphand 4.27mph, respectively. A histogram of the speeds is bell shaped.
a. Is it reasonable to apply the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean?
b. Use the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean.
c. Use the data to obtain the exact percentages of observations that lie within one, two, and three standard deviations to either side of the mean.
d. Compare your answers in parts (b) and (c).

Each of the following smooth curves represents the shape of a data set. In each case, decide whether application of the empirical rule to the data set is appropriate. Explain your answers.

Microwave Popcorn. For a given brand of microwave popcorn, what property is desirable for the population standard deviation of the cooking time? Explain your answer.

The data set has 150observations and has mean 35and standard deviation 4. Approximately how many observations lie between 31and 39?

We have provided simple data sets for you to practice finding the descriptive measures discussed in this section. For each data set.

Obtain the quartiles, determine the inter quartile range, find the five-number summary.

1,2,3,4,1,2,3,4
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