Rickets. Vitamin D is essential for strong, healthy bones. Our bodies produce vitamin D naturally when sunlight falls upon the skin, or it can be taken as a dietary supplement. Although the bone disease rickets was largely eliminated in England during the 1950s, some people there are concerned that this generation of children is at increased risk because they are more likely to watch TV or play computer games than spend time outdoors. Recent research indicated that about 20% of British children are deficient in vitamin D. Suppose doctors test a group of elementary school children.

a) What's the probability that the first vitamin D deficient child is the 8th one tested?

b) What's the probability that the first 10 children tested are all okay?

c) How many kids do they expect to test before finding one who has this vitamin deficiency?

d) They will test 50 students at the third-grade level. Find the mean and standard deviation of the number who may be deficient in vitamin D.

e) If they test 320 children at this school, what's the probability that no more than 50 of them have the vitamin deficiency?