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 (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.