6 For the adult population of the UK, 35 per cent of men and 29 per cent of women do not wear glasses or contact lenses.
- Determine the probability that, in a random sample of 40 men:
- at most 15 do not wear glasses or contact lenses;
- more than 10 but fewer than 20 do not wear glasses or contact lenses.
- Calculate the probability that, in a random sample of 10 women, exactly 3 do not wear glasses or contact lenses.
- Calculate the mean and the variance for the number who do wear glasses or contact lenses in a random sample of 20 women.
- The numbers wearing glasses or contact lenses in 10 groups, each of 20 women, had a mean of 16.5 and a variance of 2.50.
Comment on the claim that these 10 groups were not random samples.