Skodel Ltd is developing a low calorie lager for the European market with a mean designed calorie count of 43 calories per 100 ml. The new product development team are having problems with the production process and have collected an independent random sample to assess whether the target calorie count is being met (Table 4.13).

(a) Estimate the mean and variance based upon the sample data.

(b) State the value of calorie count if the production manager would like this value to be 43 ± 5%.

(c) Estimate the probability that the calorie count lies between 43 ± 5% (assume that your answers to question (a) represent the population values).

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49.7 45.9 34.3 41.4 Table 4.13 45.2 40.5 47.8 45.1 37.7 40.6 63.1 41.1 31.9 41.9 26.3 47.9 34.8 51.4 41.2 39.8 54.0 31.7