Janelle runs a janitorial service that cleans doctor's offices. Janelle tracks the hours employees spend cleaning each building. She finds for her largest building the time it
takes employees to clean the entire building has an approximately normal distribution
with a mean of 3.8 hrs and a standard deviation of 0.4 hours.
What percentage of nights does it take employees less than 3 hours to clean the largest
building?

The percentage  of nights does it take employees less than 3 hours to clean the largest  building  

 P( x < 3) = 2.28 hours

Step-by-step explanation:

Step(i):-

Given mean of the Population = 3.8 hours

Given Standard deviation of the Population = 0.4 hours

Let 'X' be the random variable in Normal distribution

Let 'X' = 3 hours

Step(ii):-

The probability that  nights does it take employees less than 3 hours to clean the largest  building

P( x < 3) = P(Z < -2)

            = 0.5 -A(-2)

           = 0.5 - A(2)

          =  0.5 - 0.4772

          = 0.0228

The probability that  nights does it take employees less than 3 hours to clean the largest  building

P( x < 3) = 0.0228

Conclusion:-

The percentage  of nights does it take employees less than 3 hours to clean the largest  building  

 P( x < 3) = 2.28   hours