86. Give the z-score for a measurement from a normal distribution for the following:
a. 1 standard deviation above the mean
b. 1 standard deviation below the mean
c. equal to the mean
d. 2.5 standard deviations below the mean
e. 3 standard deviations above the mean
142. Researchers at the University of South Florida Center for Biological Defense have developed a safe method for rapidly detecting anthrax spores in powders and on surfaces. the method has been found to work well even when there are very few anthrax spores in a powder specimen. Consider a powder specimen that has exactly 10 anthrax spores. Suppose that the number of anthrax spores in the sample detected by the new method follows an approximate uniform distribution between 0 and 10.
a. find the probability that 8 or fewer anthrax spores are detected in the powder specimen.
b. find the probability that between 2 and 5 anthrax spores are detected in the powder specimen.
The expert examines a uniform and exponential distribution. Binomial random variables for the probability distribution are discussed.