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 KKK represent the number of 'High-Precision' units in the shipment.
State a suitable distribution to model KKK.
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 VVV be the random variable representing the distributor's total profit/loss from the shipment.
Show that V=7K−60V = 7K - 60V=7K−60.
Find E(V)E(V)E(V) and Var(V)Var(V)Var(V).
Calculate P(V≥10)P(V \ge 10)P(V≥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'.
