Question

3. The Kaufman Assessment battery for children is designed to measure achievement 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.

b. What is the proportion of children will have Sequential Processing score between 90 and 110?

c. In a sample of 40 children, what is the probability the sample mean will differ from the population mean by more than 3 points (either positive or negative).

Answer #1

Given in the question

Mean. =100

Standard deviation = 15

Solution(b)

We need to find P(90<Xbar<110) = P(X<110)-P(X<90)

Z = (90-100)/15 = -0.67

Z = (110-100)/15 = 0.67

From Z table we found p-value as follows:

P(90<Xbar<110) = P(X<110)-P(X<90) = 0.7486 - 0.2514 =
0.4972

Solution(c)

No. of sample = 40

P(Xbar<97 or Xbar>103) = P(Xbar<97) + 1 -
P(Xbar<103)

Z = (103-100)/15/sqrt(40) = 3/15/sqrt(40) = 1.24

Z = (97-100)/15/sqrt(40) = -3/15/sqrt(40) = -1.24

From Z table we found

P(Xbar<97 or Xbar>103) = P(Xbar<97) + 1 - P(Xbar<103) =
0.1075 +1 - 0.8925 = 0.215

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