A random sample of 100 is taken from a population with a mean of 140 and stan- dard deviation of 25. What is the probability that the sample mean lies between 138 and 142?The Kaufman Assessment Battery for Children is designed to measure achieve- ment and intelligence with a special emphasis on nonverbal intelligence. Its global measures, such as its Sequential Processing score, are scaled to have a mean of 100 and a standard deviation of 15. Assume that the Sequential Processing score has a normal distribution. (a) Find a value such that divides the children with the highest 10% of the scores from those with the lower 90%. (b) What proportion of children will have Sequential Processing scores between 90 and 110? (c) In a sample of 20 children, what is the probability the sample mean will dif- fer from the population mean by more than 3 points (either positive or negative)