An insurance company estimates that it should make an annual profit of $150 on each homeowner’s policy written, with a standard deviation of$6000. a) Why is the standard deviation so large? b) If it writes only two of these policies, what are the mean and standard deviation of the annual profit? c) If it writes 10,000 of these policies, what are the mean and standard deviation of the annual profit? d) Is the company likely to be profitable? Explain. e) What assumptions underlie your analysis? Can you think of circumstances under which those assumptions might be violated? Explain.

An insurance company estimates that it should make an annual profit of $150 on each homeowner's policy written, with a standard deviation of$6000. What assumptions underlie your analysis? Can you think of circumstances under which those assumptions might be violated? Explain.

Find the inverse Laplace transform of the function

$$\begin{gather*} F(s) = \dfrac{5s}{(s^2 + 25)^2} \end{gather*}$$

by using the convolution theorem.

Solve each equation by the method of your choice. Simplify irrational solutions, if possible .

$$2x^2 - x = 1$$

Identify whether the given value is a statistic or a parameter.In the same study cited in the preceding exercise, 51 % of the babies were girls.

Let the life W (in years) of the usual family car have a Weibull distribution with α = 2. Show that β must equal 10 for

$$P(W > 5) = e^{-1/4} ≈ 0.7788$$

. Hint:

$$P(W > 5) = e^{-H(5)}$$

.

Identify the coordinates of four points on the line with each given slope and y-intercept. slope=-1, y-intercept=8

Factor the trinomial.

$$t ^ { 2 } - 24 t + 135$$

Solve these exercises by using the appropriate counting principle(s). A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 8 sophomores, 12 juniors, and 10 seniors are eligible to be on the committee, in how many ways can the committee be chosen?

What is the ratio of a pint of water to a quart of water?

An insurance company estimates that it should make an annual profit of $150 on each homeowner's policy written, with a standard deviation of$6000. a) Why is the standard deviation so large? b) If it writes only two of these policies, what are the mean and standard deviation of the annual profit? c) If it writes 10,000 of these policies, what are the mean and standard deviation of the annual profit?

A Gallup poll surveyed a random sample of 439 American teenagers. One question that they were asked was, "How strict are your parents compared to most of your friends' parents?" The choices were "more strict,' "less strict,” and "about the same.” The choice "more strict" was selected by 171 of the respondents . What is the research question of interest? What is the population parameter of interest? What percentage of the sample responded with "more strict"? Draw a figure to illustrate this situation

Most fungi function as ____ in their environments. A. consumers. B. producers. C. decomposers. D autotrophs.

For constants a, b, c, and d, show that the equation $x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$-2ax-2by-2cz=d describes a sphere centered at (a, b, c) with radius r, where $r ^ { 2 } = d + a ^ { 2 } + b ^ { 2 } + c ^ { 2 }$, provided $d + a ^ { 2 } + b ^ { 2 } + c ^ { 2 } \gt 0$.