1. (a) Using a calculator or computer, sketch graphs of the density function of the normal distribution p(x)=21e(x)2/(22). (i) For fixed (say, =5 ) and varying (say, =1,2,3). (ii) For varying (say, =4,5,6 ) and fixed (say, =1 ). (b) Explain how the graphs confirm that is the mean of the distribution and that is a measure of how closely the data is clustered around the mean..

1. 1. A common cause of cardiovascular disease is atherosclerosis, the hardening and narrowing of
arteries due to a buildup of plaque. For instance, significant narrowing in the coronary arteries,
which bring oxygenated blood to the heart, can produce symptoms such as chest pain, dizziness,
and breathlessness. Image by NIH: National Heart, Lung and Blood Institute [Public domain] via
Wikimedia Commons
The chart provides typical values for blood flow through a coronary artery. (a) Using Poiseuille's
Law, calculate the pressure drop across this artery. (Things to think about: How does the
pressure drop calculated in this part compare to mean arterial pressure?) Use 1mL=106m3P= (b)
Calculate the velocity of blood through this artery. Hint: How is velocity of the flow related to
flow rate? v=11sm
(c) If the artery forms blockages, the pressure drop might remain the same as above, since the
heart supplies a constant pressure. Assuming the pressure drop in a healthy coronary artery is the
same as calculated in part (a), calculate the flow rate for this artery if the radius experiences an
9.5% reduction. Q= (d) Similar to the question above: Assuming the pressure drop in a healthy
coronary artery is same as part (a), calculate the flow rate for this artery if the radius experiences
an 95% reduction. Q=smL Significance: Parts (c) and (d) show us what happens to the flow rate
of the blood for the same pressure across the artery for different amounts of blockage. How
much does the flow rate drop from (c) to (d). What implications can this have? (e) The body
quite readily accommodates to the reduction in coronary artery radius by increasing the radius of
blood vessels downstream (via auto-regulation), which reduces the overall resistance of the
circulatory system and raises the local flow rate in the coronary artery to an acceptable value.
However, as the numbers in the previous parts suggest, an 95% reduction severely reduces the
flow rate (over 99%). What if the body could maintain a flow rate of 0.8mL/s in the 95%
occluded vessel by raising the pressure? What pressure drop occurs across an 95% occluded
artery at a flow rate of 0.8mL/s ? Significance: When the blockage increases significantly, the
flow rate of the blood through the vessels decreases by a large amount. If the heart wants to
restore the flow rate to the healthy flow rate, how much pressure difference is required across the
artery. Does this pressure put strain on the heart? P=
A common cause of cardiovascular disease is atherosclerosis, the hardening and narrowing of
arteries due to a buildup of plaque. For instance, significant narrowing in the coronary arteries,
which bring oxygenated blood to the heart, can produce symptoms such as chest pain, dizziness,
and breathlessness.

2. A common cause of cardiovascular disease is atherosclerosis, the hardening and narrowing of
arteries due to a buildup of plaque. For instance, significant narrowing in the coronary arteries,
which bring oxygenated blood to the heart, can produce symptoms such as chest pain, dizziness,
and breathlessness. Image by NiH: National Heart, Lung and Blood institute [Public domain], vla
Wikimedia Commons
The chart provides typical values for blood flow through a coronary artery. (a) Using Poiseuille's
Law, calculate the pressure drop across this artery. (Things to think about: How does the
pressure drop calculated, in this part compare to mean arterial pressure?) Use 1mL=106m3. P=
(b) Calculate the velocity of blood through this artery. Hint: How is velocity of the flow related
to flow rate? v=sm
(c) If the artery forms blockages, the pressure drop might remain the same as above, since the
heart supplies a constant pressure. Assuming the pressure drop in a healthy coronary artery is the
same as calculated in part (a), calculate the flow rate for this artery if the radius experiences an
9.5% reduction. Q= (d) Similar to the question above: Assuming the pressure drop in a healthy
coronary artery is same as part (a), calculate the flow rate for this artery if the radius experiences
an 95% reduction. Q=smL Significance: Parts (c) and (d) show us what happens to the flow rate
of the blood for the same pressure across the artery for different amounts of blockage. How
much does the flow rate drop from (c) to (d). What implications can this have? (e) The body
quite readily accommodates to the reduction in coronary artery radius by increasing the radius of
blood vessels downstream (via auto-regulation), which reduces the overall resistance of the
circulatory system and raises the local flow rate in the coronary artery to an acceptable value.
However, as the numbers in the previous parts suggest, an 95% reduction severely reduces the
flow rate (over 99% ). What if the body could maintain a flow rate of 0.8mL/s in the 95%
occluded vessel by raising the pressure? What pressure drop occurs across an 95% occluded
artery at a flow rate of 0.8mL/s ? Significance: When the blockage increases significantly, the
flow rate of the blood through the vessels decreases by a large amount. If the heart wants to
restore the flow rate to the healthy flow rate, how much pressure difference is required across the
artery. Does this pressure put strain on the heart? P=Pa