The mean thickness and variance of silicon steel laminations are $0.2 mm$ and $0.02$ respectively. The varnish insulation is applied on both the sides of the laminations. The mean thickness of one side insulation and its variance are$0.1 mm$ and $0.01$ respectively. If the transformer core is made using $100$ such varnish coated laminations, the mean thickness and variance of the core respectively are
1. $30 mm$ and $0.22$
2. $30 mm$ and $2.44$
3. $40$ mm and $2.44$
4. $40 mm$ and $0.24$