The masses, www grams, of 10 artisanal chocolate bars selected at random from a production line were recorded. The following summary statistics were calculated from the sample:
∑w=824.5,∑w2=68004.5 \sum w = 824.5, \quad \sum w^2 = 68004.5 ∑w=824.5,∑w2=68004.5Calculate unbiased estimates of the mean and the variance of the masses of the chocolate bars in this production line.
Previous quality audits suggest that the masses of these chocolate bars are normally distributed with a standard deviation of 1.8 g.
Calculate a 98% confidence interval for the mean mass of chocolate bars from this line. Give the limits of your confidence interval to 2 decimal places.
A quality supervisor believes that the confidence interval in part (b) indicates that the vast majority of bars exceed a threshold of 80.5 g.
Using your results from part (b), determine the smallest proportion of chocolate bars in the production line that are expected to have a mass less than 80.5 g.
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.