6 Plastic clothes pegs are made in various colours.
The number of red pegs may be modelled by a binomial distribution with parameter \(p\) equal to 0.2 . The contents of packets of 50 pegs of mixed colours may be considered to be random samples.

1. Determine the probability that a packet contains:
   1. less than or equal to 15 red pegs;
   2. exactly 10 red pegs;
   3. more than 5 but fewer than 15 red pegs.
2. Sly, a student, claims to have counted the number of red pegs in each of 100 packets of 50 pegs. From his results the following values are calculated. Mean number of red pegs per packet \(= 10.5\)
   Variance of number of red pegs per packet \(= 20.41\)
   Comment on the validity of Sly's claim.