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.
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.