The continuous random variable TTT represents the deviation, in micrometres, of a high-precision digital caliper reading. The distribution of TTT is a continuous uniform distribution over the interval [0,2.5][0, 2.5][0,2.5].
Determine P(T<1.0)P(T < 1.0)P(T<1.0).
State the value of E(T)E(T)E(T).
Calculate Var(T)Var(T)Var(T).
A random sample of 20 readings taken by this caliper is recorded.
Find the probability that fewer than 9 of these readings show a deviation of more than 1.0 μm\mu \text{m}μm.
For a different model of caliper, the deviation X μmX \, \mu \text{m}Xμm is represented by the cumulative distribution function F(x)F(x)F(x) defined by:
F(x)={0x<00.8x−0.16x20≤x≤2.51x>2.5 F(x) = \begin{cases} 0 & x < 0 \\ 0.8x - 0.16x^2 & 0 \le x \le 2.5 \\ 1 & x > 2.5 \end{cases} F(x)=⎩⎨⎧00.8x−0.16x21x<00≤x≤2.5x>2.5Using this model, find the value of P(X>1.0)P(X > 1.0)P(X>1.0).
A large batch of 200 readings is collected from this different caliper.
Using a suitable approximation, find the probability that at least 80 of these readings show a deviation of more than 1.0 μm\mu \text{m}μm.
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.