The battery life, LLL minutes, and the total payload mass, MMM grams, of a random sample of 6 industrial drones are recorded in the table below.
| MMM (payload in g) | 200 | 400 | 600 | 800 | 1000 | 1200 |
|---|---|---|---|---|---|---|
| LLL (life in mins) | 45.5 | 40.7 | 35.9 | 31.1 | 26.3 | 21.5 |
State, with a reason, which variable is the explanatory variable.
The equation of the least squares regression line of LLL on MMM is
L=50.3−0.024M L = 50.3 - 0.024M L=50.3−0.024MGive an interpretation of the gradient of this regression line.
Find the value of Mˉ\bar{M}Mˉ and the value of Lˉ\bar{L}Lˉ.
Show that the point (Mˉ,Lˉ)(\bar{M}, \bar{L})(Mˉ,Lˉ) lies on the regression line.
Estimate the battery life of a drone carrying a payload of 750 grams.
Evaluate the reliability of the estimate calculated in part (e), justifying your answer.
The battery life of this specific drone model is assumed to be normally distributed with mean 34 minutes and standard deviation 4.2 minutes.
The central 80% of battery lives lies between aaa and bbb.
Find the value of aaa and the value of bbb to two decimal places.