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.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.