Question

the time required to clean a room in a classroom building is uniformly distributed, with a range from 9 minutes to 17 minutes. the mean and standard deviation of this distribution are:________

Answer 1

The mean time required to clean a room is 13 minutes and the standard deviation is approximately 2.31 minutes, calculated based on the properties of the uniform distribution.

Step-by-step explanation:

Since the time to clean a room is uniformly distributed between 9 and 17 minutes, we can use the properties of the uniform distribution to find the mean and standard deviation.

For a uniform distribution with lower limit a and upper limit b, the mean (or average) is calculated as (a + b) / 2 and the standard deviation is calculated as sqrt((b - a)2 / 12).

The mean time is therefore (9 + 17) / 2 = 13 minutes. And the standard deviation is sqrt((17 - 9)2 / 12) = sqrt(64 / 12) = sqrt(5.33), which is approximately 2.31 minutes.