The total duration of oxygen supply, SSS minutes, for a specific model of deep-sea diving tank is modelled by a normal distribution with a mean of 210 minutes and a standard deviation of 25 minutes.
Determine the probability that a randomly selected tank will last for more than 260 minutes.
Find the value of kkk such that P(S<k)=0.12P(S < k) = 0.12P(S<k)=0.12.
A diver has already been submerged for 260 minutes using one of these tanks. To safely reach the surface, they require a further 15 minutes of oxygen.
Calculate the probability that the tank will not run out of oxygen before the diver reaches the surface.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.