A commercial coffee machine dispenses espresso shots and steamed milk for lattes. The volume of an espresso shot, EEE ml, follows the distribution N(30.2,1.22)N(30.2, 1.2^2)N(30.2,1.22). The volume of a portion of steamed milk, MMM ml, follows the distribution N(220.5,4.52)N(220.5, 4.5^2)N(220.5,4.52). A barista prepares a "Large Latte" using a random sample of 3 espresso shots and 2 portions of steamed milk.
Find the probability that the total volume of these 5 components exceeds 540 ml.
A customer orders two portions of steamed milk to be served separately.
Determine the probability that the volumes of these two portions differ by more than 5 ml.
To calibrate the machine, a technician takes a random sample of n+1n+1n+1 espresso shots with volumes E1,E2,E3,…,En+1E_1, E_2, E_3, \dots, E_{n+1}E1,E2,E3,…,En+1. The random variable TTT is defined as
T=nE1−∑r=2n+1Er T = n E_1 - \sum_{r=2}^{n+1} E_r T=nE1−r=2∑n+1ErGiven that P(T>30)=0.0533P(T > 30) = 0.0533P(T>30)=0.0533 to 4 decimal places,
find 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.