An agricultural company monitors the weight of crop yields.
The weight, XXX kg, of a sack of potatoes is modeled by a normal distribution with a mean of 25.4 and a standard deviation of 0.8.
Find the probability that a randomly selected sack of potatoes weighs exactly 25.4 kg.
Find the probability that a randomly selected sack of potatoes weighs more than 24.5 kg.
The weight, YYY kg, of a sack of onions is modeled by a normal distribution with mean μ\muμ and standard deviation σ\sigmaσ.
Given that P(Y<12.8)=0.9P(Y < 12.8) = 0.9P(Y<12.8)=0.9, show that
12.8−μ=1.282σ 12.8 - \mu = 1.282\sigma 12.8−μ=1.282σwhere the constant is given to three decimal places. Fully justify your answer.
Given further that P(Y<10.2)=0.05P(Y < 10.2) = 0.05P(Y<10.2)=0.05, find the values of μ\muμ and σ\sigmaσ.
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.