An aerospace engineering firm produces micro-bearings for satellite sensors. The mass of these bearings is assumed to follow a normal distribution. A random sample of 8 bearings is taken, and their masses, in milligrams, are recorded as follows:
24.12,23.95,24.08,24.15,23.98,24.03,24.11,24.06 24.12, \quad 23.95, \quad 24.08, \quad 24.15, \quad 23.98, \quad 24.03, \quad 24.11, \quad 24.06 24.12,23.95,24.08,24.15,23.98,24.03,24.11,24.06Determine unbiased estimates for the population mean and the population variance of the masses of these micro-bearings.
The population standard deviation of the bearing masses is known from historical data to be 0.08 mg. The quality control team requires that for a random sample of size nnn, the probability that the sample mean mass lies within 0.015 mg of the true population mean mass is at least 0.99.
Calculate the minimum sample size n n\,n required to meet this specification.
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.