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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.