State the conditions under which the normal distribution may be used as an approximation to the binomial distribution X∼B(n,p)X \sim B(n, p)X∼B(n,p).
A production line produces "Bio-Fuse" electrical surge protectors. The company claims that 38% of these protectors are capable of absorbing a massive "Category 5" power spike.
Explain why the company would use a sample rather than testing every surge protector produced to verify this claim.
A safety board decides to investigate the claim by selecting a random sample of 400 surge protectors for rigorous spike testing.
State the hypotheses for a two-tailed test of the company's claim.
During the investigation, 172 of the 400 protectors successfully absorbed the "Category 5" spike. Using a normal approximation and a 5% level of significance, determine whether there is evidence to suggest that the company's claim is incorrect.
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.