Answer:
4.93 =< h =< 5.77
a) 90% woman (most of them) are within the height of 4.93 and 5.77 ft
b) not unusual since it is within the range
Note: for this answer, I'll use the following symbols:
=< as less or equal
=> as more or equal
Step-by-step explanation:
The inequality is
Abs[(h-5.35)/0.21)] = < 2
The absolute value sign will causes the value in the abs() bracket to be zero, whether the value is positive or negative
In other word, (h - 5.35)/0.21 could actually be a negative or positive
We consider both possibility
If it's positive: (h - 5.35)/0.21 =< 2
If it's negative: (h - 5.35)/0.21 => -2
Note that if we consider it as negative, the inequality sign change because at negative value, the order of magnitude is inverted to positive values.
Let's consider the positive first:
(h-5.35)/0.21 =< 2
h =< 2*0.21 +5.35
h =< 5.77
And then the negative
(h - 5.35)/0.21 => -2
h => -2*0.21 + 5.35
h => 4.93
From both calculation we can see that the range value of h is
4.93 =< h =< 5.77
a) this means that 90% of woman height is between 4.93 to 5.77 feet
b) 5'99'' = 5.75 ft
The height is within the range found from this calculation. So it's not that unusual.
