Chapter 8: Chapter 8

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

Calculate the standard deviation of X for each probability distribution. (You calculated the expected values in the Section 8.3 exercises. Round all answers to two decimal places.) $$ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline P(X=x) & .5 & .2 & .2 & .1 \\ \hline \end{array} $$

Classify the random variable \(X\) as finite, discrete infinite, or continuous, and indicate the values that \(X\) can take. [HINT: See Quick Examples 5-10.] According to quantum mechanics, the energy of an electron in a hydrogen atom can assume only the values \(k / 1, k / 4\) \(k / 9, k / 16, \ldots\) for a certain constant value \(k . X=\) the energy of an electron in a hydrogen atom.

In Exercises \(1-10,\) you are performing five independent Bernoulli trials with \(p=.1\) and \(q=.9 .\) Calculate the probability of the stated outcome. Check your answer using technology. [HINT: See Quick Example \(8 .\) At least three successes

In Exercises \(9-14, X\) has a normal distribution with the given mean and standard deviation. Find the indicated probabilities. $$ \mu=50, \sigma=10, \text { find } P(35 \leq X \leq 65) $$