1) According to the american cancer society, melanoma, a form of skin cancer, kills 15% of Americans who suffer from the disease each year. Consider a sample of 10,000 melanoma patients.
a) what are the expected value and variance of x, the number of the 10,000 melanoma patients who die of the affliction this year?
b) find the probability that x will exceed 1,600 patients per year.
c) would you expect x, the number of patients dying of melanoma, to exceed 6,500 in any single year? Explain.
2) Refer to the Applied Ecology and Environmental study of beech trees damaged by fungi. Recall that the researchers found that 25% of the beech trees in East Central Europe have been damaged by fungai. In an East Central European forest with 200 beech trees, how likely is it that more than half of the trees have fungi damage?
3) Suppose we want to compute the probability that between 50 and 75 of 100 white blood cells will be neutrophils, where the probability that any one cell is a neutrophil is .6. These values are chosen as proposed limits to the range of neutrophils in normal people, and we wish to predict what proportion of people will be in the normal range according to this definition.
4) Suppose a neutrophil count is defined as abnormally high if the number of neutrophils is greater than or equal to 76 and abnormally low if the number of neutrophils is less than or equal to 49. Calculate the proportion of people whose neutrophil counts are abnormally high or low.