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?

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belgrad belgrad · Answer 1 · 2020-07-20T03:48:53+02:00

Answer:

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

[tex]Z = \frac{x-mean}{S.D}[/tex]

[tex]Z = \frac{3-3.8}{0.4} = - 2[/tex]

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