The time it takes me to wash the dishes on a randomly selected night is uniformly distributed between 6 minutes and 19 minutes.

Question

The time it takes me to wash the dishes on a randomly selected night is uniformly distributed between 6 minutes and 19 minutes.

a) State the random variable in the context of this problem.

  

1. rv X = a uniform distribution
2. rv X = a randomly selected night
3. rv X = the time it takes me to wash dishes on a randomly selected night
4. rv X = washing dishes

b) Compute the height of the uniform distribution.  Leave your answer as a fraction.

   

What is the probability that washing dishes tonight will take me between 8 and 16 minutes?  Give your answer as a fraction

What is the probability that washing dishes tonight will take exactly 8 minutes?

Answer 1

x is the randomly selected night

height = 1/(19-6) = 1/13

probability between 8 and 16 = (16-8)/(19-6) = 8/13

probability is exactly 8 = 0 (since we are dealing with a continuous distribution with infinitely many points)