What is the area of the bar corresponding to a height of 67 inches in the graph, and what does the area represent in terms of probability

The probability would be 0.1193.

We compute the z-score for each end of this interval.  For the lower end, 66 inches,

z = (X-μ)/σ = (66-68)/3 = -2/3 = -0.67

For the upper end, 67 inches,

z = (X-μ)/σ = (67-68)/3 = -1/3 = -0.33

we find the area to the left of (lower than) the lower limit is 0.2514.  The area to the left of (lower than) the upper limit is 0.3707.  To find the area between these, we subtract:

0.3707 - 0.2514 = 0.1193.

Step-by-step explanation: