On the planet Pern it is the habit of dragonettes to perch on the roof of the home and "sing" when a woma inside is giving birth. Tom and Jane are expecting the birth of their child soon, and they are worried about whether the roof of their small abode can support the weight of the dragonettes. Jane's engineering calculations give 1705 pounds as a limit for their roof load. Tom's biological observations indicate that the weights of dragonettes are normally distributed with a mean of 52 pounds and a standard deviation of 8 pounds. They have noticed that typically 31 dragonettes perch on a home during the birthing time. If 31 dragonettes (randomly selected) perch on the home, what is the probability that their combined weight will exceed 1705 pounds? a) First determine this: 31 dragonettes will have a combined weight that equals 1705 pounds if they each weigh, on average, HOW MANY pounds? pounds b) The probability that a sample of 31 randomly selected dragonettes will have a mean weight greater than the number you just determined is: (Give answer correct to at least three decimal places.) c) Should Tom and Jane reinforce the roof of their house? Yes because there is more than a 5's chance the dragonettes will overload it It isn't clear what to do since there is between 1it and 5% chance of a problem No because there is less than a 1's chance the dragonettes will overload it