Decide whether the following statements are true or false. Explain your answer. a. If X has a normal distribution with $\mu = 8,$ then $P(X \geq 8.21)=P(X \leq 7.79).$ b. If X has a normal distribution, then the probability is about 0.87 that its value will be within 1.5 standard deviations of the mean.

A large mountain can slightly affect the direction of “down” as determined by a plumb line. Assume that we can model a mountain as a sphere of radius R = 2.00 km and density (mass per unit volume) 2.6 × 10³ kg/m³. Assume also that we hang a 0.50 m plumb line at a distance of 3R from the sphere’s center and such that the sphere pulls horizontally on the lower end. How far would the lower end move toward the sphere?

In a product liability case, a company can settle out of court for a loss of $350,000, or go to trial, losing$700,000 if found guilty and nothing if found not guilty. Lawyers for the company estimate the probability of a not-guilty verdict to be 0.8. a. Find the expected value of the amount the company can lose by taking the case to court. b. Should the company settle out of court?

Name the bones of the thigh, leg, ankle, and foot.

solve 240= 6z + c for c.

Suppose that $Z \sim N(0, 1)$. Find:

$$\begin{align*} &\mathbf{(a)}\, P(Z \le −0.77)\\ &\mathbf{(b)}\, P(Z \ge 0.32)\\ &\mathbf{(c)}\, P(−3.09 \le Z \le −1.59)\\ &\mathbf{(d)}\, P(−0.82 \le Z \le 1.80)\\ &\mathbf{(e)}\, P(|Z| \ge 0.91)\\ &\mathbf{(f)}\,\text{The value of } x \text{ for which } P(Z \le x) = 0.23\\ &\mathbf{(g)}\,\text{The value of } x \text{ for which } P(Z \ge x) = 0.51\\ &\mathbf{(h)}\,\text{The value of } x \text{ for which } P(|Z| \ge x) = 0.42\\ \end{align*}$$

Describe how your muscles work to help you kick a ball.

Do the ratios in each pair form a proportion? 3.5/35, 2.04/204

A plant’s response to gravity is an example of a a.Dormancy b.Hormone c.Tropism d.Critical night length

Find the derivative of each function. $f(x)=\tanh x^{2}$

What health problems are caused by air pollution?

Mrs. Nelson has a rectangular flower box that is 5 feet long and 2 feet tall. She wants the width of the box to be no more than 5 feet. If the width is a whole number, what are the possible volumes for the flower box?

A multiple-choice test is given with 5 choices (only one is correct) for each of 5 questions. Answering each of the 5 questions by guessing constitutes a binomial experiment with an associated binomial distribution. For this distribution, (A) Write the probability function. (B) Construct a table. (C) Draw a histogram. (D) Compute the mean and standard deviation.

Suppose that a dot diagram has $k$ columns and $m$ rows with $p_{j}$ dots in column $j$ and $r_{i}$ dots in row $i .$ Prove the following results. $\\$ (a)$m=p_{1}$and$k=r_{1}$(b)$p_{j}=\max \left\{i : r_{i} \geq j\right\}$for$1 \leq j \leq k$and$r_{i}=\max \left\{j : p_{j} \geq i\right\}1 \leq i \leq m .$(c)$r_{1} \geq r_{2} \geq \cdots \geq r_{m}$ (d) Deduce that the number of dots in each column of a dot diagram is completely determined by the number of dots in the rows.