A pharmaceutical company produces tablets. The mass, X X\,X mg, of the tablets follows a normal distribution N(μ,32)N(\mu, 3^2)N(μ,32). To monitor the production process, a random sample of n n\,n tablets is selected and tested at the 5% level of significance using the following hypotheses:
H0:μ=250andH1:μ>250 H_0 : \mu = 250 \quad \text{and} \quad H_1 : \mu > 250 H0:μ=250andH1:μ>250Find, in terms of nnn, the critical region of the test.
The probability of a Type II error, when the true mean is μ=252\mu = 252μ=252, is less than 0.10.
Find the minimum 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.