I solve this question by hand and have attached images for you because it is very difficult or impossible to do it here . I do it as simple as I can and make it very comprehensive for you. Hopefully, you will understand.
Note: the order for images remain same as I have attached.
<span>In triangle WXZ,
Line WY is an altitude (as shown in the attached picture)
Now, it is given that:
</span><span>If ΔYWZ ~ ΔYXW
</span>∠WXY = ∠WZY
<span>
Then, we can also conclude
</span>∠WYX = ∠WYZ = 90°....(1) (because WY is the altitude)
Now, in any triangle, the sum of all the three angles is 180.
In triangle, WXY, ∠WYX = 90° (From 1)
Therefore, WXY + XWY = 90°
Similarly, in WZY.
Hence, we conclude that XWZ is a right angle.
The Sample Mean of hours slept of the ten men asked is 8.4 hours.
The population Mean of hours slept of all the members of the theater group is 8.3 hours.