(b) A company produces cylindrical metal rods. The diameters of rods have a normal distribution with mean ucm and variance o cm. A random sample of 100 rods is taken and the diameter x, in cm, of each rod is measured. The results are summarised as Ex= 52.1 and E = 27.303. Calculate the mean and variance of the population of the diameters of the rods (i) (ii) Determine a 95% confidence interval for the mean diameter of the rods. (iv) Investigate, at the 1% significance level, whether the mean diameter of the rods is 0.512 cm.

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