Following is the probability distribution for age of a student at a certain public high school. X
13
14
15
16
17
18
P(x) 0.09 0.22 0.24 0.28 0.15 0.02

(a) Find the variance of the ages. Round the answer to at least four decimal places.
The variance of the ages is

Statements reasons 1. ab ? cd; ad ? bc 1. given 2. ac ? ac 2. reflexive property 3. ? adc ? ? cba 3. ? 4. ? dac ? ? bca; ? acd ? ? cab 4. cpctc 5. ? dac and ? bca are alt. int. ? s; ? acd and ? cab are alt. int. ? s 5. definition of alternate interior angles 6. ab ? cd; ad ? bc 6. converse of the alternate interior angles theorem 7. abcd is a parallelogram 7. definition of parallelogram what is the missing reason in step 3?