A specific chemical reaction to break down a compound follows a normal distribution with a mean time of 160 seconds and a standard deviation of 4 seconds.

(a)

What reaction time would result in a z-score of −1.5?

(b)

Using the Empirical Rule, what reaction time would have 84% of all values fall below it?

(c)

A reaction time that is shorter than 150 seconds or longer than 172 seconds will be re-run for quality control purposes. What is the probability that a reaction will need to be re-run?

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of

98.13 degrees°F

and a standard deviation of

0.53 degrees°F.

Using the empirical​ rule, find each approximate percentage below.

Modern microeconomics, specifically consumer theory, is based on utility theory—consumers maximize their utility.

Where does our modern conception of utility theory come from? (Hint: there are multiple sources.)

What is the empirical basis for utility theory?

Can utility theory be considered scientific according to Karl Popper’s conception of science?

How about Kuhn or Lakatos?

What are the criticisms of utility theory and how would its supporters (e.g., Gary Becker) respond?

Are there any alternative paradigms? What are the flaws/limitations in these approaches?

Compound X, isolated from lanolin (sheep's wool fat), has the pungent aroma of dirty sweatsocks. A careful analysis showed that compound X contains 62% carbon and 10.4% hydrogen. No nitrogen or halogen was found.

a. Compute an empirical formula for compound X.

Express your answer as a condensed structural formula.

b. A molecular weight determination showed that compound X has a molecular weight of approximately 117. Find the molecular formula of compound X.

Express your answer as a condensed structural formula.

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 37 ounces and a standard deviation of 6 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 95% of the widget weights lie between and b) What percentage of the widget weights lie between 19 and 49 ounces? % c) What percentage of the widget weights lie above 31 ? % Get help: Video LicensePoints possible: 2

You have just been hired as the marketing manager at a small retail clothing store. In the past, the store has done all the inventory purchasing, marketing and sales promotions based on intuition. Of course, as a marketing professional, you know that this is not the best strategy. You must convince your new boss to use a more empirical approach based on marketing metrics. Write a few organized paragraphs explaining to your boss what marketing metrics should be used and how they can help make decisions.

Assume the average age of an MBA student is 30.7 years old with a standard deviation of 2.2 years.

​a) Determine the coefficient of variation.

​b) Calculate the​ z-score for an MBA student who is 26 years old.

​c) Using the empirical​ rule, determine the range of ages that will include 95​% of the students around the mean.

​d) Using​ Chebyshev's Theorem, determine the range of ages that will include at least 94​% of the students around the mean.

​e) Using​ Chebyshev's Theorem, determine the range of ages that will include at least 80​% of the students around the mean.

Target-date mutual funds adopt “glide paths” such that the funds allocate investments across stocks, bonds, and other assets based on the weights that are set in the funds’ set schedules. For example, a 2050 target date fund is likely to be heavily invested in stocks relative to bonds in 2019, but the fund’s investments will gradually shift toward bonds as the year 2050 approaches. What behavior do stock market returns need to display in order for this approach to be optimal? Does the empirical evidence support or refute this required feature of returns?

It is generally believed that nearsightedness affects about 15% of children. A school district gives vision tests to 111 incoming kindergarten children. Use the empirical rule (68%-95%-99.7% Rule) to determine what proportion of nearsighted children we might expect to see in samples of 111 children (I'm not looking for the number of children). Assume conditions are met! No need to draw the model, though if you find it easier to do so you may draw it by hand and attach a picture of your model using the picture button.

The weight of an organ in adult males has a bell shaped distribution with a mean of 300 grams and a standard deviation of 20 grams. Use the empirical rule to determine the following:

a) About 99.7% of organs will be between what 2 weights?

b) What percentage of organs weigh between 260 grams and 340 grams?

c) What percentage of organs weigh less than 260 grams and more than 340 grams?

d) What percentage of organs weigh between 260 grams and 360 grams?