Question

A new drug developed to immobilize wild life is administered to 6000 buffaloes which
must be transported to another area. The buffaloes reaction time to this drug is
approximately normal with a mean of 15.4 seconds and a standard deviation of 3.4
seconds. Answer each of the following questions: Hint Draw the curve for each question.
a) What is the proportion that the reaction time is less than 16 seconds
b) How many buffaloes have a reaction time greater than 16 seconds
c) What is the proability that the reaction time will be between 13 and 24 seconds

Answer 1

(a) z = (x - µ)/σ = (16 - 15.4)/3.4 = 0.18

P (z < 0.18) = 0.57

(b) P (z > 0.18) 1 - 0.57 = 0.43

n = 0.43*6000 = 2580

(c) z = (x - µ)/σ = (13 - 15.4)/3.4 = -0.71

P (z < -0.71) = 0.2401

z = (x - µ)/σ = (24 - 15.4)/3.4 = 2.53

P (z < 2.53) = 0.9943

Probability = 0.9943 - 0.2401 = 0.7542

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