Redo please sorry for first fuzzy pic A driver\'s reaction time to visual stimul

Question

Redo please sorry for first fuzzy pic

A driver's reaction time to visual stimulus is normally distributed with a mean of 0.4 seconds and a standard deviation of 0.05 seconds. What is the probability that a reaction requires more than 0.5 seconds? What is the probability that a reaction requires between 0.4 and 0.5 seconds? Find the minimum reaction time with a probability of 90%? What are the 1^st and 3^rd quartiles, in other words, what is the maximum reaction time with probabilities 25% and 75% ?

Explanation / Answer

MEAN = 0.4

STANDARD DEVIATION = 0.05

A) P?(X>0.5) =

For x = 0.5, z = (0.5 - 0.4) / 0.05 = 2

Hence P(x > 0.5) = P(z > 2) = [total area] - [area to the left of 2]

= 1 - 0.9772 = 0.0228

B)

For x = 0.4 , z = (0.4 - 0.4) / 0.05 = 0 and for x = 0.5, z = (0.5 - 0.4) /0.05 = 2

Hence P(0.4< x <0.5) = P(0 < z < 2) = [area to the left of z = 2] - [area to the left of 0]

= 0.9772 - 0.5 = 0.4772

C) PROBABILITY = 0.90

Z SCORE = 1.3

X = MEAN + Z*STANDARD DEV = 0.4+1.3*0.05 = 0.465

D) PROBABILITY = 0.25

Z SCORE = -1.95

HENCE X = Z*STANDARD DEV + MEAN = -1.95*0.05 +0.4 = 0.302

FOR PROBABILITY = 0.75

Z SCORE = 0.7

HENCE X = Z SCORE*0.05+MEAN = 0.05*0.7+0.4 = 0.435

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