2.4.6 Probabilities using the normal distribution (A-level only)

The battery life, $L$ minutes, and the total payload mass, $M$ grams, of a random sample of 6 industrial drones are recorded in the table below.

$M$ (payload in g)	200	400	600	800	1000	1200
$L$ (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.

[1]

The equation of the least squares regression line of $L$ on $M$ is

L = 50.3 - 0.024 M

Give an interpretation of the gradient of this regression line.

[1]

Find the value of $Mˉ\bar{M}$ and the value of $Lˉ\bar{L}$ .

[2]

Show that the point $(Mˉ,Lˉ)(\bar{M}, \bar{L})$ lies on the regression line.

[2]

Estimate the battery life of a drone carrying a payload of 750 grams.

[1]

Evaluate the reliability of the estimate calculated in part (e), justifying your answer.

[1]

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 $a$ and $b$ .

Find the value of $a$ and the value of $b$ to two decimal places.

[4]

2.4.6 Probabilities using the normal distribution (A-level only) Questions