# Question: A random sample of size n 100 is taken

A random sample of size n = 100 is taken from an infinite population with the mean µ = 75 and the variance σ2 = 256.

(a) Based on Chebyshev’s theorem, with what probability can we assert that the value we obtain for X will fall between 67 and 83?

(b) Based on the central limit theorem, with what probability can we assert that the value we obtain for X will fall between 67 and 83?

(a) Based on Chebyshev’s theorem, with what probability can we assert that the value we obtain for X will fall between 67 and 83?

(b) Based on the central limit theorem, with what probability can we assert that the value we obtain for X will fall between 67 and 83?

## Answer to relevant Questions

A random sample of size n = 81 is taken from an infinite population with the mean µ = 128 and the standard deviation σ = 6.3. With what probability can we assert that the value we obtain for X will not fall between 126.6 ...Independent random samples of sizes 400 are taken from each of two populations having equal means and the standard deviations σ1 = 20 and σ2 = 30. Using Chebyshev’s theorem and the result of Exercise 8.2, what can we ...Consider the sequence of independent random variables X1, X2, X3, . . . having the uniform densities Use the sufficient condition of Exercise 8.7 to show that the central limit theorem holds. Find the probability that in a random sample of size n = 4 from the continuous uniform population of Exercise 8.46, the smallest value will be at least 0.20. With reference to Example 9.1, would the manufacturer’s decision remain the same if (a) The $ 164,000 profit is replaced by a $ 200,000 profit and the odds are 2 to 1 that there will be a recession; (b) The $ 40,000 loss ...Post your question