Making Decisions with Confidence Intervals

Assume you work for Kimberly Clark Corporation, the makers of Kleenex. The job you are presently working on requires you to decide how many Kleenexes are to be put in the new automobile glove compartment boxes. Complete the following:

1. When do people usually need Kleenexes?

2. What type of data collection technique would you use?

3. Assume you found out that, from your sample of 81 people, on average about 57 Kleenexes are used throughout the duration of a cold, with a sample standard deviation of 15. Construct a 95% confidence interval based on the data.

4. Write a brief summary interpreting your answer in part (3).

5. Explain how you will decide how many Kleenexes will go in the boxes.

A bond has a $1000 par value and issued 5 years ago. The bond has 10 years to maturity and an annual 8% annual coupon and sells for $990.

i) Estimate the bond's current yield

ii) Estimate the bond's yield-to-maturity

iii) Explain the relationship of the bond price and its yield

(Please explain the answer in detail, thank you)

transpo: Please show step by step and the diagram too. An approach to a signalized intersection has a saturation flow rate of 1800 veh/h. At the beginning of an effective red, there are 6 vehicles in queue and vehicles arrive at 900 veh/h. The signal has a 60-second cycle with 25 seconds of effective red. What is the total vehicle delay after one cycle? What is the maximum length of queuing within this cycle? (assumeD/D/1 queuing)

What can cause a phenol red indicator of carbohydrate fermentation to give a false positive with gas?

I heavily incubated my organism in the test tube and it is producing a huge gas bubble in the Durham tube and a clear yellow (acid) color. I incubated my tube at my organism's optimism growth conditions (oxygen and temperature wise) for 48 hrs exactly.. i was supposed to get a red no gas result ( -) what might have gone wrong?

For a certain​ candy, 15​% of the pieces are​ yellow, 10​% are​ red, 15​% are​ blue, 20​% are​ green, and the rest are brown. ​a) If you pick a piece at​ random, what is the probability that it

is​ brown?

it is yellow or​ blue?

it is not​ green?

it is​ striped?

​b) Assume you have an infinite supply of these candy pieces from which to draw. If you pick three pieces in a​ row, what is the probability that they

are all​ brown?

the third one is the first one that is​ red?

none are​ yellow?

at least one is​ green?

I am testing the effects of a new drug, and find that liver cells treated with this drug show the following effects:

-Reduced levels of AcCoA in the mitochondria

-Increased rates of gluconeogenesis

-Increased production of lactate

The drug, however, has no effect on Red Blood Cells (RBCs).

Why does the drug not have an effect on Red Blood Cells? What is the drug inhibiting/assisting? What other conclusions can be made with this information? (Open ended question, there are no wrong answers!)

A left turn lane is to be designed at a signalized intersection to accommodate leftturning
vehicles during the peak period of traffic. If the design peak hour volume for the left
turn movement is 150 vehicles per hour and the red time interval per signal cycle for the left turn
movement is 60 seconds.

a) Compute the average number of left turn vehicle arrivals per red interval of each signal
cycle during the design peak hour.

b) Assume that left turn vehicles arrive the intersection in a random fashion (i.e., following
Poisson distribution). Compute and plot the probability mass function (PMF) for the
number of left turn vehicles arriving during the red interval (use of Excel spreadsheets is
preferred).

c) If the design of the left-turn lane requires accommodating (or storing) the left-turn queue
95% of time during the peak hour, recommend the minimum left-turn lane length in feet
(assuming 25 feet per vehicle, including space between vehicles).

An example for numerical to categorical data off the top of my head: Light of different color has different wavelengths, but certain ranges of wavelengths qualify as certain shades/hues/tints/etc. You can generalize and say a certain range can be called "blue" or "red". Red is usually attributed to light that has a wavelength between 780 and 622 nanometers, whereas blue light is between 492 and 455 nm. To the average person, "red" and "blue" obviously mean more than a given wavelength of light, so a categorical/qualitative description might be of more use in such a context. Another example would be grading scales. Certain ranges of scores will qualify as an A, a B, and so on. Suppose you want to examine the grades of high school students admitted into a prestigious university. Students that fall in the A/B range tend to have a better chance of being admitted, while those at the other end of the spectrum are "significantly" less likely to enroll. ("Significant" here can take on the statistical meaning of the word.

1)Consider a particle that is in the second excited state of the Harmonic oscillator. (Note: for this question and the following, you should rely heavily on the raising and lowering operators. Do not do integrals.)

(a) What is the expectation value of position for this particle?

(b) What is the expectation value of momentum for this particle?

(c) What is ∆x for this particle?

2) Consider a harmonic oscillator potential.

(a) If the particle is in the state |ψ1> = √ 1/ 2 (|0> + |1>), what is <x>? <x^ 2>?

(b) If the particle is in the state |ψ2> = √ 1 /2 (|0> + |2>), what is <x>? <x ^2 >?

(c) If the particle is in the state |ψ2> = √ 1/ 3 (|0> + |2> + |3>), do you expect <x> to be zero or non-zero? What about <x^ 2 >? Why?

(d) Describe a general rule of thumb to help you quickly determine which (if any) calculations for <x>, <x^2>  will reduce to zero. Does this rule also work for <p> and <p^ 2 >?