4 Unit A2 2: Applied Mathematics (A-level only)

The battery life, $T$ minutes, of a 'Sky-Runner' delivery drone is normally distributed with mean 145 minutes and standard deviation 18 minutes.

Drones that last for more than 175 minutes are classified as having 'Extended Performance' status.

Determine the proportion of drones that achieve 'Extended Performance' status.

[3]

The manufacturer guarantees that the top 90% of drones will last at least $k$ minutes.

Find the value of $k$ .

[3]

Of the drones that achieve 'Extended Performance' status, the top $15\frac{1}{5}$ are classified as 'Ultra-Premium'.

Find the minimum battery life, $s$ , required for a drone to be classified as 'Ultra-Premium'.

[4]

A technician selects 3 drones at random from those that have achieved 'Extended Performance' status.

Find the exact probability that at least one of these drones is classified as 'Ultra-Premium'.

[2]

4 Unit A2 2: Applied Mathematics (A-level only) Questions