The heights of the trees in a forest are normally distributed, with a mean of 25 meters and a standard deviation of 6 meters. What is the probability that a randomly selected tree in the forest has a height LESS THAN OR EQUAL TO 37 meters? Use the portion of the standard normal table given to help answer the question.

A. 98.6%

B. 2.3%

C. 97.7%

D. 1.4%

Thanks for the supplied normal table; very handy.

We have random variable H with μ=25, σ=6 and we seek P(H < 37).

H=37 corresponds to a z score  (number of standard deviations from the mean) of

z = (H - μ)/σ = (37 - 25)/6 = 2

We just found out

P(H < 37) = P(z < 2)

which we can look up.  Of course for a nice round z score of 2 we don't really need to look that one up.  By the 68-95-99.7 rule, two sigma corresponds to 95%, i.e.

P(-2 < z < 2) = 95%

That means

P(0 < z < 2) = 95/2 = 47.5 %

Of course

P(z < 0) = 50%

so

P(z < 2) = P(z < 0) + P(0 < z < 2) = 50 + 47.5 = 97.5%

C

For completeness, let's look up z=2 in the table.  It doesn't say but this particular table is telling us the answer we want directly.

P(z < 2) = .9772 = 97.72%

which is a bit more accurate than the rule, but in stats that doesn't usually matter much.

B. An expression. A constant is a number within an expression with a set numerical value that cannot be changed. A variable is the letter representing an unknown number (such as x) and can be changed at any time. An expression is what contains the terms and operations, and it ALWAYS contains at least one term. :)