The random variable M M\,M represents the mass, in grams, of a synthetic gemstone produced in a laboratory. It is known that M M\,M follows a normal distribution with mean 60 and standard deviation 15.
Determine the probability that a randomly selected gemstone has a mass greater than 84 g.
Find the value of k k\,k such that
P(60−k<M<60+k)=0.90 P(60 - k < M < 60 + k) = 0.90 P(60−k<M<60+k)=0.90A single observation mmm, of MMM, is taken. A rectangular label for the gemstone's display case is designed on a coordinate grid with vertices at (0,0)(0, 0)(0,0), (m,0)(m, 0)(m,0), (m,m−20)(m, m - 20)(m,m−20) and (0,m−20)(0, m - 20)(0,m−20), where the units are centimetres.
Find the probability that the area of this label is more than 1500 cm2.
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.