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.
147 exam-style questions on OCR A Level Maths 2.4.6 Probabilities using the normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.