Question

Item 50 A farmer who grows genetically engineered corn is experiencing trouble with corn borers. A random check of 5,000 ears revealed the following: Many of the ears contained no borers. Some ears had one borer. A few had two borers, and so on. The distribution of the number of borers per ear approximated the Poisson distribution. The farmer counted 3,000 borers in the 5,000 ears. What is the probability that an ear of corn selected at random will contain no borers

Answer 1

The probability that an ear of corn selected at random with no borers is 0.5488

Given,

The farmer counted 3000 borers in the 5000 ears.

The probability mass function of Poisson distribution: $P(X=x)=\frac{e^{-\beta }\beta ^{x} }{x!}$

Here, $\beta$ is the parameter.

Then the value of parameter is:

$\beta =\frac{3000}{5000}$ = 0.6

Now determine the probability that an ear of corn selected random will contain no borers:

P(X=0) = $\frac{e^{-0.6}0.6^{*} }{0!}$

P(X=0) = $\frac{e^{-0.6} }{1}$

P(X=0) ≈ 0.5488

Learn more about probability here: brainly.com/question/14208404

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