Question 4) Application Problems Hint: You’ll need to be using Z-Scores on these

Question

Question 4) Application Problems Hint: You’ll need to be using Z-Scores on these problems! The readings speed of sixth-grade students is approximately normal, with mean speed of 120 words per minute and a standard deviation of 24 words per minute.

(a) What is the probability a randomly selected sixth-grade student reads less than 100 words per minute?

(b) What is the probability a randomly selected sixth-grade student reads more than 130 words per minute?

(c) What is the probability that a randomly selected sixth-grade reads between 100 and 130 words per minutes?

Explanation / Answer

X: The reading speed of sixth grade student per minute.

X ~ N ( mean= 120, variance= 24^2)

a) Required probability = P (X < 100 )

= P (( x-mean/S.D) < ( 100 - 120 /24))

= P (Z < - 0.8333) where Z ~ N (0,1)

From normal probability table

P (Z < -0.8333) = 0.2023   

P( X < 100 ) = 0.2023 (Answer)

b) Required probability = P ( x >130)

= P ( ( x-mean/S.D)> (130-120/24))

= P ( Z > 0.4166) where Z~ N(0,1)

From normal probability table

P ( Z > 0.4166) = 0.3385

P(X> 130) =0.3385 (Answer)

c) Required probability = P( 100 < X < 130)

= P( (100-120/24)< (x-mean/S.D) < (130-124/24))

= P ( -0.8333< Z < 0.4166)

= 1- [ P(Z< -0.8333)+P(Z > 0.4166)]

From normal probability table

P( 100 < X < 130) = 1- ( 0.2023 +0.3385)

= 0.4592

P( 100 < X < 130) = 0.4592 (Answer)

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