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Statistics Problem Set: Uniform and Exponential Distribution

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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

118. Suppose x is a binomial random variable with p=.4 and n =25. Would it be appropriate to approximate the probability distribution of x with a normal distribution?

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.

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Solution Preview

a) z=(mu+s-mu)/s=1
b) z=(mu-s-mu)/s=-1
c) z=(mu-mu)/s=0
d) ...

Solution Summary

The expert examines a uniform and exponential distribution. Binomial random variables for the probability distribution are discussed.