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Solved: Wechsler Intelligence Scale The Wechsler
Chapter 7, Problem 11RE(choose chapter or problem)
Problem 11RE
Wechsler Intelligence Scale The Wechsler Intelligence Scale for Children is approximately normally distributed, with mean 100 and standard deviation 15.
(a) What is the probability that a randomly selected test taker will score above 125?
(b) What is the probability that a randomly selected test taker will score below 90?
(c) What proportion of test takers will score between 110 and 140?
(d) If a child is randomly selected, what is the probability that she scores above 150?
(e) What intelligence score will place a child in the 98th percentile?
(f) If normal intelligence is defined as scoring in the middle 95% of all test takers, figure out the scores that differentiate normal intelligence from abnormal intelligence.
Questions & Answers
QUESTION:
Problem 11RE
Wechsler Intelligence Scale The Wechsler Intelligence Scale for Children is approximately normally distributed, with mean 100 and standard deviation 15.
(a) What is the probability that a randomly selected test taker will score above 125?
(b) What is the probability that a randomly selected test taker will score below 90?
(c) What proportion of test takers will score between 110 and 140?
(d) If a child is randomly selected, what is the probability that she scores above 150?
(e) What intelligence score will place a child in the 98th percentile?
(f) If normal intelligence is defined as scoring in the middle 95% of all test takers, figure out the scores that differentiate normal intelligence from abnormal intelligence.
ANSWER:Problem 11RE
Answer:
Step1 of 2:
We have The Wechsler Intelligence Scale for Children is approximately normally distributed, with mean 100 and standard deviation 15.
a).
The probability that a randomly selected test taker will score above 125 is P(X > 125)
Now,
P(X > 125) = 1 - P(X < 125)
= 1 - P(<
)
= 1 - P(Z < 1.66)
= 1 - 0.9515
= 0.0475.
Therefore,The probability that a randomly selected test taker will score above 125 is
P(X > 125) = 0.0475.
b).
The probability that a randomly selected test taker will score below 90 is P(X < 90)
Now,
P(X < 90) = P(X < 90)
= P(<
)
= P(Z < -0.6666)
= 0.2546.
Therefore,The probability that a randomly selected test taker will score below 90 is
P(X < 90) = 0.2546.
c).
Proportion of test takers will score between 110 and 140 is P(110 140)
Now,
P(110 < X <140) = P(110 < X < 140)
P(= P(0.6666 < Z < 2.6666)
P(Z < 2.666) = 0.9961 (Area Under Normal Curve table)
P(Z > 0.666) = 0.7454 (Area Under Normal Curve table)
P(Z < 2.666) - P(Z > 0.666) = 0.9961 - 0.7454 = 0.2507.
Therefore,Proportion of test takers will score between 110 and 140 is
P(110 140) = 0.2507.