Wingspans of adult herons have approximate normal distribution with mean 125 cm and standard deviation 12 cm. what are the first and third quartiles of the wingspans? (25% of all herons have wingspan less than the first quartile; 25% have wingspan more than the third quartile.) use these to obtain the iqr for heron wingspans.

Step-by-step explanation:

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

In this case we seek to find

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:

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