2.1. On average, a 60 minutes radio show has 45 minutes of actual programme. Let's assume that the probability distribution of the number of minutes of actual radio programme is uniformly distributed with a range of 40 minutes to 50 minutes.

i. Compute the probability that the show will have at least 48 min of actual programming time (3)

ii. Compute the standard deviation. (3)

iii. Draw the graph of f(x) clearly labelling the axes (4)

2.2. A major metropolitan newspaper selected a simple random sample of 2000 readers from their list of 20000 subscribers. They asked whether the paper should increase its coverage of local news. Seventy percent of the sample did not support the idea of more local news coverage.

What is the 94% confidence interval for the proportion of readers who would like more coverage of local news? (10)

2.3. The operations manager of a computer accessories firm with branches in Cape Town and Durban wants to establish whether their Cape Town branch is performing better than their Durban branch in terms of the average size of orders received. Both branches have been operating for only one year. A random sample of 17 orders from the Cape Town branch had an average value of R335.20 with a standard deviation equal to R121.50. Orders received by the Durban branch of the firm were also randomly sampled. The average of the 15 orders sampled was R265.60 with a sample standard deviation of R152.20.

Can the operations manager conclude, at the 5% significance level, that the Cape Town branch is performing better than the Durban branch? Show the null and alternative hypotheses for the test and draw the appropriate conclusion.