A factory manufactures precision-calibrated weights for laboratory use. They produce two standard masses: Type A and Type B. The weight of a Type A mass, XXX g, follows the distribution N(12.50,0.082)N(12.50, 0.08^2)N(12.50,0.082). The weight of a Type B mass, YYY g, follows the distribution N(24.20,0.122)N(24.20, 0.12^2)N(24.20,0.122). A random sample of 3 Type A masses and 5 Type B masses is selected for quality control testing.
Find the probability that the combined weight of these 8 masses is greater than 159.0 g.
A random sample of 2 Type B masses is selected.
Find the probability that the difference between the weights of these 2 Type B masses is more than 0.15 g.
A random sample of n+1n+1n+1 Type A masses is taken, with weights X1,X2,X3,…,Xn+1X_1, X_2, X_3, \dots, X_{n+1}X1,X2,X3,…,Xn+1. The random variable TTT is defined as
T=nX1−∑r=2n+1Xr T = n X_1 - \sum_{r=2}^{n+1} X_r T=nX1−r=2∑n+1XrGiven that P(T>8.1)=0.0062P(T > 8.1) = 0.0062P(T>8.1)=0.0062 to 4 decimal places,
calculate the value of nnn.
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.