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 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.