Answer
No, it does not.
Work Step by Step
In order to create a box and whisker plot, use a box a whisker plot maker online. (To draw one by hand, draw a line, making the far left point the minimum and the far right point the maximum. Then, draw a box, where the left side of the box is $Q_1$ and where the right side of the box is $Q_3$. Finally draw a vertical line through the box: this is your median.) Doing this, we find the following five number summary:
1497
1538
1550
1571
1642
While the five number summary shows that the histogram is roughly symmetric, meaning that the data are roughly evenly spread out, this only indicated, but does not mandate, that the data are roughly bell-shaped, for one cannot conclude that the data are bell-shaped based on a box and whisker plot.
