Question

To be considered abnormal height a 30 year old must be 1.2 feet below average or 1.2 feet above average. If the average height is 5.1 feet, at what heights (in interval notation) would a 30 year old be considered abnormal? O [0,3.7) or (6.5,00) 0 (3.9,6.3] 0 (0,3.9] or [6.3,00) 0 (3.9,6.3)​

Answer 1

A 30-year-old would be considered of abnormal height if they are below 3.9 feet or above 6.3 feet. The interval notation for these heights is (0, 3.9] or [6.3, ∞).

Step-by-step explanation:

To determine at what heights a 30-year-old would be considered of abnormal height, we use the average height provided (5.1 feet) and calculate the heights that are 1.2 feet below and 1.2 feet above this average.

For the lower bound, we subtract 1.2 from 5.1:
5.1 ft - 1.2 ft = 3.9 ft.
This means anyone below 3.9 ft would be considered abnormally short.

For the upper bound, we add 1.2 to 5.1:
5.1 ft + 1.2 ft = 6.3 ft.
This means anyone above 6.3 ft would be considered abnormally tall.

Therefore, using interval notation, the heights at which a 30-year-old would be considered abnormal are:
(0, 3.9] or [6.3, ∞).