# Chapter 8: Chapter 8

Problem 70

Suppose you take larger and larger samples of a given population. Would you expect the sample and population standard deviations to get closer or further apart? Explain.

Problem 70

If \(X\) is a random variable, what is the difference between a sample mean of measurements of \(X\) and the expected value of \(X ?\) Illustrate by means of an example.

Problem 71

In one Finite Math class, the average grade was 75 and the standard deviation of the grades was \(5 .\) In another Finite Math class, the average grade was 65 and the standard deviation of the grades was \(20 .\) What conclusions can you draw about the distributions of the grades in each class?

Problem 72

You are a manager in a precision manufacturing firm and you must evaluate the performance of two employees. You do so by examining the quality of the parts they produce. One particular item should be \(50.0 \pm 0.3 \mathrm{~mm}\) long to be usable. The first employee produces parts that are an average of $50.1 \mathrm{~mm}\( long with a standard deviation of \)0.15 \mathrm{~mm}$. The second employee produces parts that are an average of \(50.0 \mathrm{~mm}\) long with a standard deviation of \(0.4 \mathrm{~mm}\). Which employee do you rate higher? Why? (Assume that the empirical rule applies.)

Problem 73

If a finite random variable has an expected value of 10 and a standard deviation of 0, what must its probability distribution be?

Problem 74

If the values of \(X\) in a population consist of an equal number of 1 s and \(-1\) s, what is its standard deviation?

Problem 75

\- Find an algebraic formula for the population standard deviation of a sample \(\\{x, y\\}\) of two scores \((x \leq y)\).

Problem 76

\- Find an algebraic formula for the sample standard deviation of a sample \(\\{x, y\\}\) of two scores \((x \leq y)\).

Problem 8

In exercise, you are performing 5 independent Bernoulli trials with \(p=.1\) and \(q=.9 .\) Calculate the probability of each of the stated outcomes. Check your answer using technology. At least four successes

Problem 8

Compute the mean, median, and mode of the data samples \(4.2,-3.2,0,1.7,0\)