The time it takes me to wash the dishes is uniformly distributed between 11 minutes and 17 minutes.
What is the probability that washing dishes tonight will take me between 12 and 14 minutes?
Give your answer accurate to four decimal places.
straightforward ....
find z scores for both 12 and 14 minutes
go to the chart, look up the two z-scores proabilities, then subtract them
I assumed you know how to find the mean and sd for the given information.
.09
To find the probability that washing dishes tonight will take between 12 and 14 minutes, we can use the concept of uniform distribution. In a uniform distribution, all outcomes between the minimum and maximum values have equal probabilities.
Given that the time it takes to wash dishes is uniformly distributed between 11 and 17 minutes, we can calculate the probability as follows:
1. Calculate the range of the distribution, which is the difference between the maximum and minimum values:
Range = Maximum Value - Minimum Value
= 17 minutes - 11 minutes
= 6 minutes
2. Find the probability of the desired range within this distribution:
Probability = (Desired Range) / (Total Range)
Desired Range = 14 minutes - 12 minutes
= 2 minutes
Probability = 2 minutes / 6 minutes
≈ 0.3333 (to 4 decimal places)
Therefore, the probability that washing dishes tonight will take between 12 and 14 minutes is approximately 0.3333.