Answered: We know that certain bacteria are…

We know that certain bacteria are present in water in a proportion of 3 bacteria per cm3 . What is the probability that a sample of 10 cm3 contains 10 bacteria?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

We know that certain bacteria are present in water
in a proportion of 3 bacteria per cm3
. What is the probability that a sample of 10 cm3
contains 10 bacteria?

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Expert Solution

Step 1: Determine the given variable

Given:
$lambda equals 3 space b a c t e r i a space p e r space cm cubed$ . This means that on average, we expect to find 3 bacteria in each cubic centimeter of water.
For a $10 space cm cubed$ sample, the expected number of bacteria, or the mean, would be $lambda cross times 10 equals$ 30 bacteria.

This is a Poisson distribution problem. The Poisson distribution gives the probability of a given number of events happening in a fixed interval of time or space, given a known average rate of occurrence. In this case, our "interval" is the volume of water $open parentheses 10 space cm cubed close parentheses$ and the rate is $lambda equals 3$ bacteria per $cm cubed$ .

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