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 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.