standard deviation

Question

Peter and Sally each shoot 12 arrows at a target that is circular with a diameter of 72 inches. the mean of the distances that Peter's arrows strike from the center of the target is 20 inches, and the standard deviation of his distance is 3 inches. The mean of the distances that Sally's arrows strike from the center of the target is 16 inches, and the standard deviation of her distances is 4 inches. What statements can be made about the region of the target that at least 75 percent of Peter's arrows strike and the region of the target that at least 75 percent of Sally's arrows strike?

Answer 1

The new target is reduced by 75% will make it to be 54ich from 72inch.

Therefore using proportions to keep the same mean or average we would get that peter is even closer to target now his average is located at a mean of (20*54)/72= 15inches is the new mean which is closer than 20inchesto target and the new Sd would be (15*3)20=2.25inches. Now Sally is even closer to target therefore her new mean would be (16*54)72= 12inches close to target which is 3 inches closer than Peter. Her Sd would be (12*4)/16= 3. Showing how close each target is from each other so Peters arrows are closer to each other than Sally's but are farther from the target than Sally's.