Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5.

Find the mean and standard deviation of the weights.

Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5. Do these data satisfy the assumptions for inference? Explain.

Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5.

Comment on the company's stated net weight of 28.3 grams.

Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5. Comment on the company's stated net weight of 28.3 grams.

The weights in kilograms of twelve students are:

$$\begin{array}{lllllllll}{63} & {76} & {99} & {65} & {63} & {51} & {52} & {95} & {63} & {71} & {65} & {83}\end{array}$$

When one student leaves the class, the mean weight of the remaining 11 students is 70 kg. Find the weight of the student who left.

Body weights and backpack weights were collected for eight students.

These data were entered into a statistics package and least-squares regression of backpack weight on body weight was requested. Here are the results:

$$\begin{array}{lrrrr}\text { Predictor } & \text { Coef } & \text { Stdev } & \text { t-ratio } & p \\ \text { Constant } & 16.265 & 3.937 & 4.13 & 0.006 \\ \text { BodyWT } & 0.09080 & 0.02831 & 3.21 & 0.018 \\ \text { s }=2.270 & \text { R-sq }=63.2 \% & \text { R-sq(adj) }=57.08\end{array}$$

The computer output reports that s=2.270. This is an estimate of the parameter $\sigma$. Use the formula for s to verify the computer's value of s.

Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28., 28.9, 29.1, 29.5. a) Do these data satisfy the assumption for inference? Explain. b) Find the mean and standard deviation of the weights. c) Create a 95% confidence interval for the mean weight of such bags of chips. d) Explain in context what your interval means. e) Comment on the company's stated net weight of 28.3 grams.

Piecewise Functions-Weight Above and Below Earth's Surface Problem: When you are above the surface of Earth, your weight is inversely proportional to the square of your distance from the center of Earth. This is because the farther away you are, the weaker the gravitational force between Earth and you. When you are below the surface of Earth, your weight is directly proportional to your distance from the center. At the center you would be "weightless" because Earth's gravity would pull you equally in all directions.

The mentioned figure shows the graph of the weight function for a 150 lb person. The radius of Earth is about 4000 mi. The weight is called a piecewise function of the distance because it is given by different equations in different "pieces" of the domain. Each piece is called a branch of the function. The equation of the function can be written

$$y= \begin{cases}a x & \text { if } 0 \leq x \leq 4000 \\ \frac{b}{x^2} & \text { if } x \geq 4000\end{cases}$$

Find the values of a and b that make y = 150 when x = 4000 for each branch.

Consider the following data and corresponding weights.

$$\begin{matrix} x_i & \text{Weight} (w_i)\\ \text{3.2} & \text{6}\\ \text{2} & \text{3}\\ \text{2.5} & \text{2}\\ \text{5} & \text{8}\\ \end{matrix}$$

Compute the sample mean of the four data values without weighting. Note the difference in the results provided by the two computations.

Let $v_1, v_2, \ldots, v_n$ denote the vertices of the complete graph ${K}_n, n \geq 3$, and give edge $v_i v_j$ weight $i+j$. Find a minimum spanning tree for this weighted graph and the weight of such a tree.

The following table shows the weights of six objects and their values.

$$\begin{array}{lcccccc} \text {Weight} & 2 & 2.5 & 3 & 3.5 & 4 & 4.5 \\ \hline \text {Value} & 12 & 11 & 7 & 13 & 10 & 11 \end{array}$$

If your knapsack holds a maximum weight of 9, what is the highest value you can pack in?

The weights in kilograms of twelve students are: 63 76 99 65 63 51 52 95 63 71 65 83 Calculate the mean weight of the students.

Prove that any minimum weight spanning tree in a connected weighted graph can be obtained by Kruskal's algorithm.

The average weight of an airline passenger’s suitcase is 45 pounds. The standard deviation is 2 pounds. Assume the weights are normally distributed. If an airline handles 2,000 suitcases in one day, find the number that will weigh less than 43.5 pounds.