Write formulas that express the central tendency and variability of the population of all possible sample proportions. Explain what each of these formulas means in your own words.

Draw a Lewis structure for each of the following molecules or ions. Describe the electron-pair geometry and the molecular geometry around the central atom.\

$$\mathrm{SF}_4$$

Find the measure of a central angle $\theta$ (in radians) that intercepts an arc of length $s= 20 \textrm{ mm}$ on a circle with radius $r=100 \textrm{ cm}$ .

How many lone pairs are there on the central atom in the Lewis structure of $\mathrm{ICl}_2^{-}$?

(a) $0$

(b) $1$

(c) $2$

(d) $3$

(e) $4$

The weights of the fish caught by a fisherman were in pounds:

$$1.7,1.8,3.0,1.8,3.5,3.1,3.3$$

Which measure of central tendency would the fisherman use to represent his fishing most favorably?

Draw the Lewis structure, and then specify the electron-pair and molecular geometries for each of the following molecules or ions. Identify the hybridization of the central atom.\

$$\mathrm{XeF}_4$$

A composite transposon integrated in a circular plasmid occasionally transposes the DNA comprising the original plasmid rather than the transposon's central region. Explain how this is possible.

In a body-centered cubic unit cell, the central atom lies on an internal diagonal of the cell and touches the comer atoms.
(c) Derive an expression for $a$ in terms of $r$.

Find the area of a sector of a circle having radius $r$ and central angle $\theta$. See the example in this section.

$$r=18.3 \mathrm{~m}, \theta=125^{\circ}$$

These exercises involve the formula for the length of a circular arc. A circular arc of length 25 ft subtends a central angle of

$$50 ^ { \circ }$$

. Find the radius of the circle.

For following, write the Lewis structure(s), predict the molecular structure (including bond angles), and give the expected hybridization of the central atom.

$$\mathrm{O}_3$$

Sketch the resonance structures for the nitrate ion, $NO _3{ }^{-}$. Is the hybridization of the $N$ atom the same or different in each structure? Describe the orbitals involved in bond formation by the central $N$ atom.

These exercises involve the formula for the area of a circular sector. The area of a sector of a circle with a central angle of

$$140 ^ { \circ }$$

is

$$70 \mathrm { m } ^ { 2 }$$

. Find the radius of the circle.

A box contains N identical gas molecules equally divided between its two halves. Does the time spent in the central configuration increase or decrease with an increase in N?