A certain tennis player makes a successful first serve $70\%$ of the time. Assume that each serve is independent of the others. She serves 80 times in a match. What 's the probability she makes at least 65 first serves?

You are an explorer on an alien plant and find an island chain inhabited by several species of what you decide to call “Snarfs.” Some strongly resemble mainland Snarfs but others are quite different. Hypothesize how colonization and speciation occurred.

Reread the first paragraph under the heading " Native Americans of North America ." How is your culture group different from others? How is it the same? Use this knowledge to describe how Native American cultures were the same and different.

A diet center claims that it has the most effective weight loss program in the region. Its advertisements say, "Participants in our program lose more than 5 pounds within a month." Six clients of this program are weighed on the first day of the diet and then one month later.

$$\begin{array}{|c|c|c|} \hline \text { Client } & \text { Weight on First Day of Diet } & \text { Weight One Month Later } \\ \hline 1 & 158 & 151 \\ \hline 2 & 205 & 200 \\ \hline 3 & 170 & 169 \\ \hline 4 & 189 & 179 \\ \hline 5 & 149 & 144 \\ \hline 6 & 135 & 129 \\ \hline \end{array}$$

a. Specify the null and alternative hypotheses that test the diet center's claim.

b. Assuming that weight loss is normally distributed, calculate the value of the test statistic.

c. Find the p-value.

d. At the $5 \%$ significance level, do the data support the diet center's claim?

A diet center claims that it has the most effective weight loss program in the region. Its advertisements say, "Participants in our program lose more than 5 pounds within a month." Six clients of this program are weighed on the first day of the diet and then one month later.

$$\begin{array}{|c|c|c|} \hline \text { Client } & \text { Weight on First Day of Diet } & \text { Weight One Month Later } \\ \hline 1 & 158 & 151 \\ \hline 2 & 205 & 200 \\ \hline 3 & 170 & 169 \\ \hline 4 & 189 & 179 \\ \hline 5 & 149 & 144 \\ \hline 6 & 135 & 129 \\ \hline \end{array}$$

b. Assuming that weight loss is normally distributed, calculate the value of the test statistic.

A certain tennis player makes a successful first serve 70% of the time. Assume that each serve is independent of the others. If she serves 6 times, what's the probability she gets all 6 serves in?

A certain tennis player makes a successful first serve 70% of the time. Assume that each serve is independent of the others. If she serves 6 times, what's the probability she gets at least 4 serves in?

A certain tennis player makes a successful first serve $70\%$ of the time. Assume that each serve is independent of the others. If she serves 6 times, What are the four conditions that need to be met to justify your answers for the earlier exercise?

If $Z$ is a standard normal variable, find the probability that $Z$ lies between $-1.10$ and $-0.36$.

$a)~ 0.4951$.

$b)-0.2237$.

$c)~0.2237$.

$d)~0.2239$.

Solve:

A soccer player has been successful $60 \%$ of the times she kicks toward goal. If she has taken $80$ kicks, what percent will she have if she kicks $11$ out of the next $20$ ?

Is there a function f which has the following partial derivatives? If so what is it? Are there any others?

$$\begin{aligned} & f_x(x, y)=4 x^3 y^2-3 y^4 \\ & f_y(x, y)=2 x^4 y-12 x y^3 . \end{aligned}$$

A certain tennis player makes a successful first serve 70% of the time. Assume that each serve is independent of the others. If she serves 6 times, what's the probability she gets

a) all 6 serves in?

b) exactly 4 serves in?

c) at least 4 serves in?

d) no more than 4 serves in?

Some strings of Christmas lights are connected in series, and others are connected in parallel. Which is less affected by the burning out of one light bulb? Explain your reasoning.

Solve the differential equation. It can be solved by the method of undetermined coefficients, but others cannot.

$$y^{\prime \prime}+y=\cot x, \quad 0<x<\pi$$