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2.4.4 Mean and variance of the binomial (A-level only)

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Question 39

A logistics company finds that 35% of their long-distance delivery drones require a battery recalibration after each flight.

a.

State a distribution that is suitable to model the number of drones requiring recalibration in a random selection of 20 drones.

[1]
b.

State two conditions for the distribution in part (a) to be a valid model.

[2]
c.

Find the probability that: exactly 8 drones in a selection of 20 require recalibration,

[2]
d.

Find the probability that: fewer than 12 drones in a selection of 40 require recalibration.

[2]
e.

A maintenance supervisor notes that the technical team will be overwhelmed if more than 100 drones in a daily batch of 250 require recalibration.

Using a suitable approximation, find the probability that the technical team will be overwhelmed in a particular batch of 250 drones.

[4]

2.4.4 Mean and variance of the binomial (A-level only) Questions

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