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'.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.