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 (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.