Answer
a) Mean:140. Standard deviation:8.37.
b)It is unusually low. The touch therapist doesn't seem to have any special ability.
Work Step by Step
In this case the probability of guessing well is 0.5.
a) Mean=$n\cdot p=280 \cdot 0.5=140$.
Standard deviation: $\sqrt{n \cdot p \cdot (1-p)}=\sqrt{280 \cdot 0.5 \cdot 0.5}=8.37.$
b) If a value is unusual, then it is more than two standard deviations far from the mean. $Minimum \ usual \ value=mean-2\cdot(standard \ deviation)=140-2\cdot8.37=123.26$
$Maximum \ usual \ value=mean+2\cdot(standard \ deviation)=140+2\cdot8.37=156.74$.
123 is less than the lower bound, therefore it is an unusually low value. The touch therapist's 'ability' made things worse than randomly guessing the hand, therefore the touch therapist doesn't seem to have any special ability.
