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'.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.