What is the probability that there will be exactly 18 plants in a two-acre region?

1.   A chemist wishes to estimate the concentration of particles in a certain suspension. She withdraws 3 mL of the suspension and counts 48 particles. Estimate the concentration in particles per mL and find the uncertainty in the estimate.

2.  A microbiologist wants to estimate the concentration of a certain type of bacterium in a waste-water sample. She puts a 0.5 mL sample of the wastewater on a microscope slide and counts 39 bacteria. Estimate the concentration of bacteria, per mL, in this wastewater, and find the uncertainty in the estimate.

3.  Two-dimensional Poisson process. The number of plants of a certain species in a certain forest has a Poisson distribution with mean 10 plants per acre. The number of plants in T acres therefore has a Poisson distribution with mean 10T.

a.  What is the probability that there will be exactly 18 plants in a two-acre region?

b.  What is the probability that there will be exactly 12 plants in a circle with radius 100 ft? (1 acre = 43,560 ft 2 .)

c.    The number of plants of a different type follows a Poisson distribution with mean λ plants per acre, where λ is unknown. A total of 5 plants are counted in a 0.1 acre area. Estimate λ, and find the uncertainty in the estimate.

 

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