You are working as a leader of a mountain rescue team. often hikers and climbers 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.

in order to get your team members better prepared for what to expect at rescue scenes, you decided to determine the rate of body mass loss based on your team's past operation record. focused on healthy adults of body mass in the range from 55 kg to 70 kg (before they get lost in the mountain), you collected four cases and the data are in the table below.

tlost (days) mloss (kg) r (kg/day)
case 1 3.2 10.1 3.16
case 2 3.4 8.67 2.55
case 3 3.5 9.66 2.76
case 4 3.2 10.6 3.31
in the above table, the first column tlost is the number of days the person survived without food until the rescue, the second column mloss is the amount of body mass loss of the person. the body mass loss rate r is calculated as r = mloss/tlost and given in the third column.

hint : keep your final numerical answers to at least 3 significant figures regardless of how many figures the input numbers have.

(d) what is the relative error in the determination of the body mass loss rate r?

(e) based on the body mass loss rate determined from the data in the above table, if a healthy adult is to survive without food for tlost = 4.50 ± 0.1 days, what is the most likely amount of body mass loss mloss of the person at rescue?
mloss = kg

(f) what is the error estimate of the body mass loss in part (e)?
σmloss = kg

(g) if a healthy person with normal body mass mi = 60.4 ± 0.3 kg is to survive for exactly 6 days without food, what is the person's expected body mass at rescue mf?
mf = kg

(h) what is the standard error of the mean for the value of mf calculated in part (g)?
σmf = kg

(i) what is the relative error σmf / mf ?