The lengths, LLL mm, of precision-machined alloy rods are modeled by a normal distribution with mean 24.0 mm24.0\text{ mm}24.0 mm and standard deviation 0.5 mm0.5\text{ mm}0.5 mm.
Find P(L>25.1)P(L > 25.1)P(L>25.1).
Find, to one decimal place, the value of kkk such that P(L<k)=3P(L>k)P(L < k) = 3 P(L > k)P(L<k)=3P(L>k).
Write down the name given to the value of kkk.
For a different grade of rod, the lengths are normally distributed with mean 30.0 mm30.0\text{ mm}30.0 mm.
Given that the 90th percentile for this grade of rod is 31.922 mm31.922\text{ mm}31.922 mm,
find the standard deviation of the length of this grade of rod.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.