Explain what you understand by the Central Limit Theorem.
A lightbulb manufacturer monitors the lifespan of their LED bulbs. It is known that the standard deviation of the bulb lifespans is 1200 hours. A random sample of 64 bulbs is tested, and the total sum of their lifespans is recorded as ∑x=1,510,400\sum x = 1,510,400∑x=1,510,400 hours.
Calculate a 99% confidence interval for the mean lifespan of an LED bulb.
Explain the relevance of the Central Limit Theorem in your calculation in part (b).
The manufacturer claims that the bulbs are designed to last for an average of 24,000 hours. A consumer advocacy group suggests that the bulbs are failing much sooner than advertised.
Comment on the advocacy group's suggestion based on your confidence interval. Give a reason for your answer.
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.