At fast-food restaurants, the lids for drink cups are made with a small amount of flexibility, so they can be stretched across the mouth of the cup and then snugly secured. When lids are too small or too large, customers can get frustrated, especially if they end up spilling their drinks. At one restaurant, large drink cups require lids with a diameter of between 3.95 and 4.05 inches. The restaurant's lid supplier claims that the diameter of the large lids follows a normal distribution with mean 3.98 inches and standard deviation 0.02 inches. Assume that the supplier's claim is true.

What percent of large lids have diameters between 3.95 and 4.05 inches?

At fast-food restaurants, the lids for drink cups are made with a small amount of flexibility, so they can be stretched across the mouth of the cup and then snugly secured. When lids are too small or too large, customers can get frustrated, especially if they end up spilling their drinks. At one restaurant, large drink cups require lids with a diameter of between 3.95 and 4.05 inches. The restaurant's lid supplier claims that the diameter of the large lids follows a normal distribution with mean 3.98 inches and standard deviation 0.02 inches. Assume that the supplier's claim is true.

What percent of large lids are too small to fit?

Scores on the Wechsler Adult Intelligence Scale (a standard IQ test) for the 20 to 34 age group are approximately Normally distributed with

$$\mu = 110$$

and

$$\sigma = 25.$$

What percent of people aged 20 to 34 have IQs between 125 and 150?

At fast-food restaurants, the lids for drink cups are made with a small amount of flexibility, so they can be stretched across the mouth of the cup and then snugly secured. When lids are too small or too large, customers can get frustrated, especially if they end up spilling their drinks. At one restaurant, large drink cups require lids with a diameter of between 3.95 and 4.05 inches. The restaurant's lid supplier claims that the diameter of the large lids follows a normal distribution with mean 3.98 inches and standard deviation 0.02 inches. Assume that the supplier's claim is true. Let X = the diameter of a randomly selected large lid from this supplier. Find and interpret $P(3.95 \leq X \leq 4.05).$

At fast-food restaurants, the lids for drink cups are made with a small amount of flexibility, so they can be stretched across the mouth of the cup and then snugly secured. When lids are too small or too large, customers can get frustrated, especially if they end up spilling their drinks. At one restaurant, large drink cups require lids with a diameter of between 3.95 and 4.05 inches. The restaurant's lid supplier claims that the diameter of the large lids follows a normal distribution with mean 3.98 inches and standard deviation 0.02 inches. Assume that the supplier's claim is true.

Compare your answers to previous parts. Does it make sense for the lid manufacturer to try to make one of these values larger than the other? Why or why not?

Scores on the Wechsler Adult Intelligence Scale (a standard IQ test) for the 20 to 34 age group are approximately Normally distributed with

$$\mu = 110$$

and

$$\sigma = 25.$$

At what percentile is an IQ score of 150?

At some fast-food restaurants, customers who want a lid for their drinks get then from a large stack near the straws, napkins, and condiments. The lids are made with a small amount of flexibility so they can be stretched across the mouth of the cup and then snugly secured. When lids are too small or too large, customers can get very frustrated, especially if they end up spilling their drinks. At one particular restaurant, large drink cups require lids with a "diameter" of between 3.95 and 4.05 inches. The restaurant's lid supplier claims that the diameter of its large lids follows a Normal distribution with mean 3.98 inches and standard deviation 0.02 inch. Assume that the supplier's claim is true. Put a lid on it! What percent of large lids are too big to fit?

At fast food restaurants, the lids for drink cups are made with a small amount of flexibility so they can be stretched across the mouth of the cup and then snugly secured. When lids are too small or too large, customers can get frustrated, especially if they end up spilling their drinks.

At $1$ restaurant, large drink cups require lids with a diameter of between $3.95$ and $4.05$ inches. The restaurant's lid supplier claims that the diameter of the large lids follows a normal distribution with mean $3 .98$ inches and standard deviation $0. 02$ inches. Assume that the supplier 's claim is true:

• a. What percent of large lids are too small to fit?
• b. What percent of large lids are too big to fit?
• c. What percent of large lids have diameters between $3. 95$ and $4. 05$ inches?
• d. Compare your answers to parts a and b. Does it make sense for the lid manufacturer to try to make $1$ of these values larger than the other? why or why not.

The rate law for the reaction in which 1 mol of cyclobutane $(C_4 H_8)$ decomposes to 2 mol of ethylene $(C_2 H_4)$ at 1273 K is Rate = (87 $s^{−1}$) $[C_4 H_8]$. What is the instantaneous rate of this reaction when $\left[\mathrm{C}_{4} \mathrm{H}_{8}\right]=0.0100 \mathrm{mol} / \mathrm{L} ?$

Perform the indicated operation. Simplify, if possible.

$$\frac{x-2}{6}-\frac{x+1}{3}$$

Perform the indicated operation. Then simplify :

$$8 \div 2 \frac{2}{3}$$

An efficiency study of the morning shift at a certain factory indicates that an average worker who arrives on the job at 8:00 A.M. will have assembled

$$f(x)=-x^{3}+6 x+15 x^{2}$$

iPads x hours later $(0 \leq x \leq 8)$. (a.) How many units will such a worker have assembled by 10:00 A.M.? (b.) How many units will such a worker assemble between 9:00 A.M. and 10:00 A.M.?

A city's population is 1000 and growing at $5\%$ a year.Find a formula for the population at time $t$ years from now assuming that the $5\%$ per year is an:
(i) Annual rate (ii) Continuous annual rate

The largest interval $I$ over which the explicit solutions $\phi_1(x) = \sqrt{25-x^2}$ and $\phi_2(x)=-\sqrt{25-x^2}$ of

$$\dfrac{dy}{dx} = \dfrac{x}{y}$$

are defined is the open interval $(-5, 5)$. Why can't the interval $I$ of definition be the closed interval $[- 5, 5]$?