Find the probability that the height of a randomly selected tree is between 220.9 ft and 246 ft. P(220.9 < X < 246)

Answer 1

In this type of problem, you would (for a normal distribution) need values for the mean

or average height of the measured trees as well as the standard deviation (or variation)

of measured heights from that average.

If given a mean of 230 and a standard deviation of 8, you would compute:

(220.9 − 230) ÷ 8 equal to -1.1375; and

(246.0 − 230) ÷ 8 equal to 2.

You would then take these "Z-values" of -1.1375 & 2 and go to a

Table Of Proportions Of Area Under The Standard Normal Curve.

This table will give probabilities of 0.4772498681 for Z = 2 and

-0.3723353377 for Z = -1.1375.

[These values are generated by a Power Series from Calculus on a programmable

calculator and are extremely accurate; a table from a book will only go to 3 or 4

decimal places.]

The probability that you seek is then given by (0.4772498681 − -0.3723353377)

or 0.8495852058.

0.8495852058 is fairly close to 1, which indicates "dead certainty" in Probability,

whereas 0 indicates "complete impossibility".

The probability that the height of a tree falls between 220.9 feet and 246 feet is

then considered high for this problem.