A company produces a certain type of mug. The masses of these mugs are normally distributed with mean $\mu$ and standard deviation 1.2 grams. A random sample of 5 mugs is taken and the mass, in grams, of each mug is measured. The results are given below.

$229.1 \quad 229.6 \quad 230.9 \quad 231.2 \quad 231.7$

(a) Find a 95% confidence interval for $\mu$, giving your limits correct to 1 decimal place.

Sonia plans to take 20 random samples, each of 5 mugs. A 95% confidence interval for $\mu$ is to be determined for each sample.

(b) Find the probability that more than 3 of these intervals will not contain $\mu$.