15.27 Reaction times. The time that people require to react to a stimulus usually has a right-skewed distribution, because lack of attention causes a few lengthy reaction times. Reaction times for children with attention deficit hyperactivity disor der (ADHD) are more skewed, because their condition causes more frequent lack of attention. In one study, children with ADHD were asked to press the spacebar on a computer key board when any letter other than X appeared on the screen.

With 2 seconds between letters, the mean reaction time was 445 milliseconds (ms) and the standard deviation was 82 ms."
Take these values to be the population fj, and cr for ADHD children.

(a) What are the mean and standard deviation of the mean reaction time x for a randomly chosen group of 15 ADHD chil dren? For a group of 150 such children?

(b) The distribution of reaction time is strongly skewed. Ex plain briefly why we hesitate to regard x as Normally distributed for 15 children but are willing to use a Normal distribution for the mean reaction time of 150 children.

(c) What is the approximate probability that the mean reaction time in a group of 150 ADHD children is greater than 450 ms?