Nine year old Emily Rosa conducted this test: A professional touch therapist put both hands by cardboard partition and Emily would employ a coin toss to randomly choose one of the hands. Emily would place her hand just above the hand of therpist, who was then asked to recognize the hand that Emily had selected. The touch therapists believed that they could sense energy field and recognize the hand that Emily had selected. The trial was repeated 280 times.(Based upon the data from " A close loooko at therapeutic touch," by rosa, Journal of American Medical Association
a. Supposing that the touch therapist have no special powers and made random guesses, find out the mean and standard deviation for numbers of correct responses in group of 280 trials.
b. The professional touch therapist recognized the correct hand 123 times in 280 trials. Is tha result unusual ? What does tht result suggest regarding the capability of touch therapists to choose the correct hand by sensing an energy field?