A chemical company produces two types of liquid fertilizer, 'GrowthPlus' and 'LeafBloom'. The volume, G G\,G ml, of 'GrowthPlus' used in a standard sprayer is modelled by G∼N(12.2,1.22)G \sim N(12.2, 1.2^2)G∼N(12.2,1.22). The volume, L L\,L ml, of 'LeafBloom' used in a standard sprayer is modelled by L∼N(5.8,0.52)L \sim N(5.8, 0.5^2)L∼N(5.8,0.52).
Two sprayers, one with each type of fertilizer, are selected independently at random. Find the probability that the volume of 'GrowthPlus' used is more than double the volume of 'LeafBloom' used.
'LeafBloom' is sold in 900 ml bottles. Assume that the volumes used by the 150 standard sprayers are independent. Find the probability that one bottle will be sufficient for 150 standard sprayers.
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.