## Answers

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 X_{1} ~ N ( = 30, = 5 )

and X_{2} ~ N ( = 50, = 8)

Where X_{1} = reading test score

and X_{2} = math test score.

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

for x_{1} = 37

for x_{2} = 56

Since z_{1} > z_{2} , therefore, Johnny is better in reading than the math.

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r2-30 56- 50 6/80.75

.
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