A factory manufactures precision-calibrated weights for laboratory use. They produce two standard masses: Type A and Type B. The weight of a Type A mass, XXX g, follows the distribution N(12.50,0.082)N(12.50, 0.08^2)N(12.50,0.082). The weight of a Type B mass, YYY g, follows the distribution N(24.20,0.122)N(24.20, 0.12^2)N(24.20,0.122). A random sample of 3 Type A masses and 5 Type B masses is selected for quality control testing.
Find the probability that the combined weight of these 8 masses is greater than 159.0 g.
A random sample of 2 Type B masses is selected.
Find the probability that the difference between the weights of these 2 Type B masses is more than 0.15 g.
A random sample of n+1n+1n+1 Type A masses is taken, with weights X1,X2,X3,…,Xn+1X_1, X_2, X_3, \dots, X_{n+1}X1,X2,X3,…,Xn+1. The random variable TTT is defined as
T=nX1−∑r=2n+1Xr T = n X_1 - \sum_{r=2}^{n+1} X_r T=nX1−r=2∑n+1XrGiven that P(T>8.1)=0.0062P(T > 8.1) = 0.0062P(T>8.1)=0.0062 to 4 decimal places,
calculate the value of nnn.
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.