You just started working as a member of a mountain rescue team.
Your team's main objective is to rescue the hikers and climbers who
get lost in the mountain, sometimes for days without food. From
your team's past operation record, you have learned that those who
survived for days without food suffer a significant loss in their
body mass.
You are tasked to prepare public awareness information based on
your team's past operation record, to alert hikers and climbers on
what to expect if they get lost without food.
Focused on healthy adults of body mass in the range from 55 kg to
70 kg (before they get lost in the mountain), you tabulated five
cases and the data are in the table below.
t_{lost} (days) | R (kg/day) | |
---|---|---|
case 1 | 2.6 | 2.80 |
case 2 | 3.4 | 3.44 |
case 3 | 2.1 | 3.09 |
case 4 | 1.9 | 3.34 |
case 5 | 3.6 | 3.06 |
In the above table, the first column t_{lost} is
the number of days the person survived without food until the
rescue, the second column R is the rate of body mass loss
while the person is lost in the mountain until the rescue. The unit
of body mass loss rate is kg/day.
Hint : Keep your final numerical answers to at
least 3 significant figures regardless of how many figures the
input numbers have.
(a) Based on the data in the above table, what is the most likely
time period people have to survive without food once they get lost
in the mountain? In other words, what is the average value of
t_{lost}?
t_{lost} = days
(b) What is the sample standard deviation of
t_{lost}?
s_{tlost} =
days
(c) What is the standard error of the mean for the value determined
for t_{lost}?
σ_{tlost} =
days
(d) What is the relative error in the determination of
t_{lost}?
From the statistical analysis of the data in the second column in
the above table, you found that the body mass loss rate is
R = 3.15 ± 0.113 kg/day. Now you want to calculate the
most likely amount of net body mass loss ΔM if they get
lost in the mountain. You decided to calculate with the equation,
ΔM = R×t_{lost}.
(e) What is the most likely body mass loss ΔM of those who
your team would rescue?
ΔM = kg
(f) What is the error estimate in the determination of
ΔM?
σ_{ΔM} = kg
(g) What is the relative error in the determination of
ΔM?
While you are preparing the public awareness information, your team
has left on a rescue mission. The missing person's normal body mass
is M_{i} = 60.1 ± 0.5kg based on the information
that the person submitted voluntarily at the entry to the mountain.
Since you now know the most likely body mass loss ΔM of
those who your team would rescue, you want to estimate the person's
body mass at rescue M_{f} using the equation
M_{f} = M_{i} - ΔM.
(h) What is the most likely body mass of the person at rescue,
M_{f}?
M_{f} = kg
(i) What is the error estimate for the value determined for
M_{f}?
σ_{Mf}
= kg
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