1. A 0.6% phenol solution was used to disinfect a 3-hour culture of Bacillus paratyphosus, the organism that causes paratyphoid fever. Triplicate subsamples of the culture were taken at various times after the addition. The ean numbers of viable organisms were 129, 112, 81, 78, 64, 38, 19, 12, and 1 at 1, 2, 4, 5, 7, 10, 15, 20, and 32 minutes, respectively.
a. What proportion of the organisms died every minute?
b. If the culture contained 8 ´ 105 viable bacteria/ml when the disinfectant was added, how long was it until 99.9% of the organisms were killed?
2. A vial of sodium phosphate solution labeled with radioactive 32P (the half-life of 32P is 14.3 days) arrived in one of our labs this morning.
How much of this solution will have to be used in an experiment this afternoon to provide an activity of 250 mCi, given that it had an activity of 500 mCi/ml when tested 10 days ago?
3. Twinning percentage in California dairy herds currently ranges from 3 to 7% of calvings. (To demonstrate the expected range in probabilities, evaluate them for twinning percentages of both 3 and 7 %.)
a. Assuming an average calving interval of 12 months and an average herd life of three lactations (three calvings), how likely is it that a single "average" cow never twins?
b. How likely is it that an "average" cow has more than one set of twins in her lifetime?
4. A sampling of plots in a young forest yielded a mean density of 2.5 tree seedlings per plot with a variance of 2.7.
a. How compatible are these statistics with the assumption that a random (Poisson) spatial pattern of seedlings existed in the young forest?
b. What percentages of plots would be expected to contain no seedlings, exactly 1 seedling, exactly 2 seedlings, or less than 3 seedlings if a Poisson distribution was assumed?