Question

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?

Answer 1

To find the percentage of nights that take employees less than 3 hours to clean the largest building, we need to use the normal distribution and calculate the area under the curve to the left of 3 hours. The percentage of nights that take employees less than 3 hours to clean the largest building is approximately 2.28%.

Step-by-step explanation:

To find the percentage of nights that take employees less than 3 hours to clean the largest building, we need to use the normal distribution and calculate the area under the curve to the left of 3 hours.

First, we need to standardize the value of 3 hours using the formula z = (x - mean) / standard deviation. In this case, the mean is 3.8 hours and the standard deviation is 0.4 hours. Plugging in the values, we get z = (3 - 3.8) / 0.4 = -2.

Next, we use a standard normal distribution table or calculator to find the area to the left of z = -2. From the table or calculator, we find that the area to the left of z = -2 is approximately 0.0228, or 2.28%.

Therefore, the percentage of nights that take employees less than 3 hours to clean the largest building is approximately 2.28%.

Answer 2

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

`Z = (x-mean)/(S.D)`

`Z = (3-3.8)/(0.4) = - 2`

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