Question 67 – 2.4.13 Model with probability distributions - Questions

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'.

2.4.13 Model with probability distributions

Question 54

2.4.13 Model with probability distributions

Question 54

2.4.13 Model with probability distributions

Question 54

2.4.13 Model with probability distributions Questions

2.4.13 Model with probability distributions

Question 54

2.4.13 Model with probability distributions Questions