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.
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.