The volume of liquid, in ml, in a bottle of water is normally distributed with mean μ\muμ and standard deviation 6.46.46.4. Given that 5%5\%5% of bottles contain less than 490 ml490\text{ ml}490 ml, find:
the value of μ\muμ to two decimal places.
the percentage of bottles that contain more than 510 ml510\text{ ml}510 ml.
The bottling machine is recalibrated so that the volume of liquid is normally distributed with mean 500500500 and standard deviation σ\sigmaσ.
Given that 95%95\%95% of bottles contain between 495 ml495\text{ ml}495 ml and 505 ml505\text{ ml}505 ml, find the value of 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.