Red Widget Strategies wants to improve its customer service by being more efficient in how...

klupko5HR

klupko5HR

Answered

2022-12-05

Red Widget Strategies wants to improve its customer service by being more efficient in how phone calls are processed. Toward that end, Red Widget does a statistical analysis of 1,000 outbound phone calls. The length of the calls is normally distributed, with a population mean = 240 seconds, and a population standard deviation = 40 second.
a. What is the probability that a particular call lasted less than 180 seconds?
b. What is the probability that a particular call lasted between 180 and 300 seconds?
c. What is the probability that a call lasted between 110 and 180 seconds?
d. What is the probability that a call lasted more than 300 seconds?

Answer & Explanation

greffhc

greffhc

Expert

2022-12-06Added 7 answers

Solution:
Given that,
μ = 240  σ = 40  N = 1000
 p ( x < 180 )  = p ( x  μ σ ) < ( 180  240 40 )  = p ( z <  60 40 )  = p ( z <  1. 5 )
Using z table
= 0.0668  N  = 0.0668  1000
Probability = 66.8
b) p ( 180 < x < 300 )  = p ( 180  240 40 ) < ( x  μ σ ) < ( 300  240 40 )  = p (  60 40 < z < 60 40 )  = p (  1.5 < z < 1.5 )  = p ( z < 1.5 )  p ( z < 1.5 )
Using z table
= 0.9332  0.0668  = 0.8664  N  = 0.8664  1000
Probability = 866.4
c) p ( 110 < x < 180 )  = p ( ( 110  240 40 ) < ( x  μ σ ) < ( 180  240 40 )  = p (  130 40 < z <  60 40 )  = p (  3.25 < z <  1.5 )  = p ( z <  1.5 )  p ( z <  3.25 )
Using z table
= 0.0668  0.0006  = 0.0662  N  = 0.0662  1000
Probability = 66.2
d) p ( x > 300 )  = 1  p ( x < 300 )  = 1  p ( x  μ σ ) < ( 300  240 40 )  = 1  p ( z < 60 40 )  = 1  p ( z < 1. 5 )
Using z table
= 1  0.9332  = 0.0668  N  = 0.0668  1000
Probability = 66.8

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