Question

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.

	tlost (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

Answer 1