State the conditions under which the normal distribution may be used as an approximation to the binomial distribution.
A manufacturer of electric components claims that 45% of their batch of sensors are high-precision.
Explain why the company should not test every sensor produced to verify this claim.
To test the manufacturer's claim, a random sample of 300 sensors was tested.
State the hypotheses for a two-tailed test of the company’s claim.
Given that 150 of the 300 sensors were found to be high-precision,
use a normal approximation to test, at the 10% level of significance, whether or not the manufacturer's claim is justified.
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.