The masses, yyy grams, of 15 dragon fruits randomly sampled from a large harvest were measured and recorded. The following summary statistics were obtained:
∑y=6750,∑y2=3042450 \sum y = 6750, \quad \sum y^2 = 3042450 ∑y=6750,∑y2=3042450Calculate unbiased estimates of the mean and the variance of the masses of the dragon fruits in the harvest.
Agricultural research suggests that the masses of these dragon fruits follow a normal distribution with a standard deviation of 18 g.
Calculate a 95% confidence interval for the mean mass of dragon fruits in the harvest. Give the limits of your confidence interval to 2 decimal places.
The farm manager claims that the results in part (b) indicate that it is highly unlikely for a fruit to weigh less than 420 g.
Use your answer to part (b) to estimate the smallest proportion of dragon fruits in the harvest that are expected to have a mass less than 420 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.