2. A random sample of receipts for individuals eating at the Terrace Restaurant showed the sample mean to be = $10.39 with sample standard deviation s = $2.15. Use Chebyshev's Theorem to find the smallest interval centered on the mean in which we can expect at least 88.9% of the data to fall.

2. A random sample of receipts for individuals eating at the Terrace Restaurant showed the sample mean to be = $10.39 with sample standard deviation s = $2.15. Use Chebyshev's Theorem to find the smallest interval centered on the mean in which we can expect at least 88.9% of the data to fall.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

2. A random sample of receipts for individuals eating at the Terrace Restaurant showed
the sample mean to be = $10.39 with sample standard deviations =
$2.15.
Use Chebyshev's Theorem to find the smallest interval centered on the mean in
which we can expect at least 88.9% of the data to fall.

Expert Solution

Step 1

Consider that a random variable X has expected value x̄ and standard deviation, s. Now, according to Chebyshev’s Inequality, it can be said that:

P(| X – x̄ | < ks) ≥ 1 – (1/k²), where k is any positive real number.

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