The following boxplot summarizes the heights of a sample of 100 trees growing on a tree farm. The figure presents a graph of a boxplot over a number line titled Tree Height, in inches. The numbers 28 through 44, in increments of 2, are indicated. The data represented by the boxplot is as follows. Note that all values are approximate. The left whisker extends from 33 through 34. The box extends from 34 through 38, and a vertical line segment at 36 breaks the box into 2 parts. The right whisker extends from 38 through 43.
Emily claims that a tree height of 43 inches is an outlier for the distribution. Based on the 1.5×IQR rule for outliers, is there evidence to support the claim?

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diana156

04.03.2022

Mathematics

A Poisson distribution, with λ=5.3

$P(x) = \frac{\lambda^{x} *e^{-\lambda}}{x!}$

Step-by-step explanation:

For this type of random variables, a Poisson distribution is the most adecuate.

If the number of occurrences in ten minutes is 5.3, we can define the parameter λ=5.3 and the probability function as:

$P(x) = \frac{\lambda^{x} *e^{-\lambda}}{x!} =\frac{5.3^{x} *e^{-5.3}}{x!} \approx\frac{0.005*5.3^{x}}{x!}$

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