Question

3. A high school with 1200 students is placing students with an IQ score of 130 and above in an accelerated class. A standardized IQ test has a mean of 100 and a standard deviation of 15. Assuming a normal population, approximately how many students will be assigned to the accelerated class? 4. A reading test has a mean of 30 and a standard deviation of 5. A math test has a mcan of 50 and a standard deviation of 8. Johnny scored 37 on the reading test and 56 on the math test. Did he perform better in math or reading, relative to his classmates?

Answer 1

3. Let X = IQ score.

Therefore from the given information

X ~ N ( = 100, )

Here first we need to find P( X > 130) = 1 - P(X < 130) ....( 1 )

for x = 130, the corresponding Z score is as follows:

therefore P(Z < 2 ) = 0.9772

Plug this value in equation ( 1 ) , we get:

P( X > 130) = 1 - 0.9772 = 0.0228

Here n = 1200

Therefore, required answer is 1200*0.0228 = 27.36 = 27 (approximately).

4) Here X₁ ~ N ( = 30, = 5 )

and X₂ ~ N ( = 50, = 8)

Where X₁ = reading test score

and X₂ = math test score.

For comparison we need to find z score for each test scores.

for x₁ = 37

for x₂ = 56

r2-30 56- 50 6/80.75

Since z₁ > z₂ , therefore, Johnny is better in reading than the math.