APPLIED STATISTICS QUESTIONS

Homework

Chapter 15: Exercises 15-1 through 15-3 (page 314 of the text)
EXERCISES

· 15-1Using the following data set on hospital admissions, define the service area for Hospital A, based only on quantitative factors (Table 15-5).

· 15-2Compute the target bed capacity of Cheswick Community Hospital 10 years from now, based on the following information:

Assume current population of Cheswick Community Hospital’s service area = 145,000

Assume projected population increase of 8% in service area over the next 10 years.

Table 15-5Hospital Admissions, by Community

Assume a future admission rate per 1000 of 102.

Assume average length of stay of 4.7 days in 10 years. Assume a target occupancy rate of 78% in 10 years.

· 15-3Newgroveton is a community of 445,000. In the most recent year, there were 750 new cases of disease A in the community. Assume the expected incidence rate for disease A is 245 per 100,000 people. Was the community’s experience better or worse than expected? Explain your answer.

· 15-4The population of South Winslet is 358,000. Assume the following physician distribution by specialty in the community (Table 15-6).

Assume that one half of physicians retire at the age of 65 and all physicians retire at age 70.

How many physicians, by specialty will we must recruit in 5 years? Ten years?

Table 15-6Exercise 15-4

EXERCISES

Derive an expression to estimate the distance L attainable in the long jump, in terms of the approach velocity V. Neglect air drag and assume that planting the foot at the beginning of the jump does not generate a vertical force but rather produces the optimal angle for takeoff. Find L for V = 10 m/s. (Note: you will have to determine the optimum angle.)

Consider the standing high jump, but this time the jumper is on the moon, where the local gravitational field is one sixth that on earth: g _moon = g/6.

(a) Using an analysis similar to that developed in Section 10.1.1, derive a formula for the height that a person’s center of gravity can be elevated in the standing high jump on the moon,

(b) If J. C. Evandt were to repeat his record-breaking jump on the moon, what bar height could he clear? To compute this height, you may use the same data and assumptions as were used in the text.

A 75 kg stunt man executes a standing jump with the aid of a harness and support wire. In addition to the constant 1100 N force his legs exert during the push-off phase, the wire has a lift mechanism that applies a force given by 550e^−s/L (in Newtons), where L is 0.4 m and s is the distance traveled. The lift mechanism is engaged at the bottom of the crouch (where s = 0) and a safety catch detaches the wire when the stuntman leaves the ground.

(a) For a crouch depth of 0.4 m, compute the maximal elevation of his center of gravity.

(b) If the safety catch fails to disengage, show that his center of gravity is elevated 0.462 m at the top of the jump.

Recall the example in Section 8.4.2 about the person lifting a weight and the resulting stresses in the bones of the forearm. Assuming there is a 0.01 mm defect in the radius bone 8 cm from the elbow, determine how many times the subject can lift the weight before his/her bone fractures. Does your calculation likely overestimate or underestimate the actual number of lifts? Why

Recall that several experimental studies have demonstrated that the yield strain of trabecular bone is relatively constant over a wide range of apparent densities. Demonstrate that this is the case using the density dependency relationships in Section 9.3 and Hooke’s law, which is valid for trabecular bone virtually up to the yield strain.

In your own words, describe the main events occurring between the arrival of an action potential at a motor neuron end plate and contraction of the corresponding muscle. Use 250 words or less.

You are standing on the top of Mount Everest (elevation 29 028 ft; 8708 m) where atmospheric pressure is 235 mmHg and the ambient temperature is 0 ◦C. The air composition is 78.6% N2, 20.8% O2, 0.04% CO2, and 0.50% H2O. Treat the air as an ideal gas.

(a) If you remove your oxygen set, how many times per minute must you breathe so as to satisfy your O₂ requirements of 284 ml/min at BTP? (Recall that BTP is 1 atmosphere and 37 ◦C). Assume that you take in tidal volumes of 1000 ml (at ambient conditions) and that you can transfer only 30% of the O₂ into your blood.

(b) Assuming that you could breathe that fast, what would the composition of the expired air be? Your CO₂ production rate is 227 ml/min at BTP, and expired air is fully humidified. (Partial pressure of water vapour at 37 ◦C and 100% relative humidity is 47 mmHg.)

This question is concerned with mass transfer in the whole lung.

(a) If you switch from breathing air to breathing xenon, what is the minimum number of breaths after which the concentration of xenon in your lungs is 99%, by volume? Assume that no xenon diffuses out of the lungs, that perfect mixing occurs in the lungs, and that the xenon environment is so large that the exhaled air does not change the xenon concentration of 100%.

(b) If you switch back to an air environment and breathe normally, after how many breaths is the xenon concentration in your lungs reduced to 0.1%, by volume?

Consider mass transfer from pulmonary capillaries to a single alveolus. Suppose that, in addition to the normal 0.6 μm thick tissue layer between the blood and the air, scar tissue has formed that is 1μm thick. The effective diffusivity of CO₂ in this scar tissue is 0.7 × 10⁻⁶ cm²/s. When CO² has to cross both the “normal” tissue and the scar tissue, the mass transfer efficiency of the alveolus is reduced. Considering the entire alveolus, compute the net percentage reduction in blood-to-air CO² transfer due to the scar tissue for a 50 μm long capillary. Note: you do not need to re-derive equations; you should be able to make some simple modifications to equations in the text to get what you need. Remember that when two mass transfer barriers are in series, their mass transfer resistances add. You may use parameter values (except for capillary length) given in Section 7.4.1.

In Section 4.3.7, we derived an expression for the ratio of pressure pulses at a junction when the two daughter tubes were identical. Perform the same calculation assuming that the two daughter tubes have different characteristic impedances. Specifically, what are the ratios R and T? To simplify the notation, call Z₀ the impedance of the parent tube, and Z₁, Z₂ the impedances of the two daughter tubes.

A patient who has normal blood pressure (systolic and diastolic) also has hardening of the arteries, including the brachial artery in the upper arm. Will this patient’s measured blood pressure be larger than the actual value, and why or why not?

In Section 4.2.3 we concluded that the pumping power of the human heart is approximately 2 W (assuming a normal cardiac output of 5 liters/min). Like any pump, however, the heart is not 100% efficient, and, therefore, the power that is supplied to the heart muscle will actually exceed 2 W. In this question we will estimate the heart’s pumping efficiency η by calculating how much energy is supplied to the heart muscle from the blood. (Note that the heart muscle has its own vasculature, called the coronary circulation.)

(a) When we calculated the pumping power of the heart, we only considered the head gain across the heart from the pressure increase. In general, there could also be changes in elevation (very small) and in kinetic energy. Estimate the ratio of kinetic energy head to pressure head at peak systole, when pressure is 120 mmHg and blood velocity is 100 cm/s. Can we safely neglect kinetic energy gains in calculating pumping power?

(b) At rest, the coronary blood flow is 225 ml/min, and 65% of the O₂ is removed from the blood as it passes through the coronary vasculature. The oxygen capacity of blood is 19.4 ml O2/100 ml blood, and in a normal diet 4.83 kcal of food energy is released for every liter of O₂ consumed. From this data, estimate η for the heart. State assumptions.

(c) The basal metabolic rate of a normal individual is 72 kcal/h. What fraction of this is consumed by the heart?