A shipment contains 30 custom-built sensor units. Each unit has a probability of 0.2 of being classified as 'High-Precision'. Let the random variable $K$ represent the number of 'High-Precision' units in the shipment.

State a suitable distribution to model $K$ .

A distributor makes a profit of £5 on each 'High-Precision' unit but loses £2 on every unit that is not 'High-Precision' due to recalibration costs. Let $V$ be the random variable representing the distributor's total profit/loss from the shipment.

Show that $V = 7 K - 60$ .

Find $E (V)$ and $V a r (V)$ .

Calculate $\ge 10)$ .

A larger production facility produces 200 sensor units. The facility manager claims that for this specific batch, the probability of a unit being 'High-Precision' is 0.15.

Using a suitable approximation, estimate the probability that at least 40 units in this batch are 'High-Precision'.

State a suitable distribution to model $K$ .

Show that $V = 7 K - 60$ .

Find $E (V)$ and $V a r (V)$ .

Calculate $\ge 10)$ .

A larger production facility produces 200 sensor units. The facility manager claims that for this specific batch, the probability of a unit being 'High-Precision' is 0.15.

Using a suitable approximation, estimate the probability that at least 40 units in this batch are 'High-Precision'.

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

Question 27

Markscheme

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

Question 27

Markscheme

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

Question 27

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

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

Question 27

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