Numerade

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(Statistics Review) (a) Suppose a random variable $x$ follow a normal distribution of $N[0, (\frac{1}{3})^2]$. If we let $w = 3x$, what is the distribution of $w$? Let $z = 9x^2 = (3x)^2$, what is the distribution for $z$? Find the mean of the random variable $z$, i.e. $E(z)$. [Hint: use the property of the normal distribution and Chi-square distribution in Lecture Note 1.]

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Anhydrides are _____ reactive than acid chlorides, but _____ reactive than other carboxylic acid derivatives. Multiple choice question. more; less less; more

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Consider the experiment of tossing two balanced coins. Find the probability observing at least one tail. A) $1/4$ B) $1/2$ C) $3/4$ D) $2/3$

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A firm's demand curve for labor shifts when O the wage rate changes O the number of available workers changes O wages rise faster than productivity. O the price of its output changes O none of the answers are correct.

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You work for a large company, where the goal is to have over 85% job satisfaction. You wish to do a hypothesis test to see if the goal is met. A simple random sample of 131 employees was asked that question, and their responses are recorded in the spreadsheet linked at the top of the exam. You used data in the spreadsheet linked above to test the hypothesis. What is your decision and conclusion at the .05 significance level? Group of answer choices Fail to reject the null; there is insufficient evidence that the satisfaction rate is above 85% for the whole company. Reject the null; there is insufficient evidence that the satisfaction rate is above 85% for the whole company. Assumptions not met Reject the null; there is sufficient evidence that the satisfaction rate is over 85% for the whole company. Fail to reject the null; there is sufficient evidence the satisfaction rate is above 85% for the whole company.

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Each of the following frequency tables represents a data set. Which of these frequency tables represents the data set with the smallest standard deviation? \begin{tabular}{|c|c|c|} \hline (A) & Value & Frequency \\ \hline 4 & 0 \\ \hline 5 & 10 \\ \hline 6 & 40 \\ \hline 7 & 10 \\ \hline \end{tabular} (B) \begin{tabular}{|c|c|} \hline Value & Frequency \\ \hline 4 & 8 \\ \hline 5 & 14 \\ \hline 6 & 16 \\ \hline 7 & 14 \\ \hline 8 & 8 \\ \hline \end{tabular}

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Give a fully simplified expression for $\sin(\tan^{-1}(\frac{x}{7}))$.\newline Your answer should have no trigonometric functions.

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What annual percent growth rate is equivalent to a continuous percent growth rate of 6% ?

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Integrate the intensity of the equation. $I = \left(\frac{\mu_0 \alpha^2 E_0^2 \omega^4}{32\pi^2 c}\right)\frac{\sin^2 \theta}{r^2}$ on a spherical surface far from the dipole to find the total power radiated by it. (Where $\theta$ is the axial angle of the spherical coordinates, here $\alpha$ it plays a role like the susceptibility $\chi$ and is called \"polarizability.\" And $E_0$ is the amplitude of the incident field. The corresponding intensity radiated by the dipole is (the magnitude of the time average of the Poynting vector)).

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Given the graph of $f'(x)$ below, the critical points of $f(x)$ can be found when: $x = -2$ and $x = 2$ $x = 2$ $x = 0$ $x = -2, x = 0, x = 2$

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jennifer a.