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Garden canes have lengths that are normally distributed with mean 208.5cm and standard deviation 2.5cm. what is the probability of the lenght of a randomly selected cane being between 205cm and 210cm

Respuesta :

The probability of randomly selecting a can between 205cm to 210cm is 0.8765

Data;

  • Mean = 208.5cm
  • standard deviation = 2.5cm

Normal Distribution

To solve this problem, we can simply use the formula of probability and substitute the value.

[tex]p\frac{(205-108.5)}{2..5} < \frac{x - 208.5}{2.5} < \frac{210 - 205.5}{2.5}\\p(-1.4 < z < 1.8)[/tex]

Rearranging the equation and solving for the z-values;

[tex]p(z < 1.8-p < z < -1.4)[/tex]

This becomes

[tex]p = 0.9641 - 0.0876 = 0.8765[/tex]

The probability of randomly selecting a can between 205cm to 210cm is 0.8765

Learn more on normal distribution here;

https://brainly.com/question/4079902

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