Question

wingspans of adult herons have approximate normal distribution with mean 125cm and a standard deviation 12cm. what proportion of herons have wingspan of excatly 140cm?

Answer 1

`P (X = 140) = 0`

Explanation:

We know that the heron wingspan follow a normal distribution with an mean of 125 cm.

In this case we seek to find

`P (X = 140)`

If X is a random variable that represents the length of the heron wingspan, then X follows a normal distribution and therefore is a continuous random variable.

Then by definition of continuous random variable we have to:

`P (X = a) = 0` where a is a constant.

That is to say that only the ranges of values can have a different probability of zero. The probability that a continuous random variable is equal to some exact value is always zero.

Finally we can conclude that

`P (X = 140) = 0`