he length of conversations between supervisors and workers in a certain manufact

Question

he length of conversations between supervisors and workers in a certain manufacturing industry is normally distributed with a mean of 4.0 minutes and a standard deviation of 0.8 minutes. Use the normal curve table to determine the percentage of conversations that are longer than 4.4 minutes, longer than 5 minutes, longer than 3 minutes, and shorter than 2 minutes. he length of conversations between supervisors and workers in a certain manufacturing industry is normally distributed with a mean of 4.0 minutes and a standard deviation of 0.8 minutes. Use the normal curve table to determine the percentage of conversations that are longer than 4.4 minutes, longer than 5 minutes, longer than 3 minutes, and shorter than 2 minutes.

Explanation / Answer

Solution:- Given that mean = 4 ,sd = 0.8 " Formula : Z = (X - mu)/s"

a) P(X < 4.4) = P(Z < (4.4 - 4)/0.8)
= P(Z < 0.5)
= 1 P(Z < 0.5)
= 1 0.6915
= 0.3085
= 30.85%

b) P(X < 5) = P(Z < (5 - 4)/0.8)
= P(Z < 1.25)
= 1 P(Z < 1.25)
= 1 0.8944
= 0.1056
= 10.56%

c) P(X < 3) = P(Z < (3 - 4)/0.8)
= P(Z > 1.25)
= P(Z < 1.25)
=0.8944
= 89.44

d) P(X > 2) = P(Z > (2-4)/0.8)
= P (Z < 2.5)
= 1 P(Z < 2.5)
= 1 0.9938
= 0.0062
= 0.62%

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