STATS HELP PLEASE

Question

I need help with STATS homework please. I tried twice already on A thinking that the random variable was a "random selected night" however it tells me that this is wrong for the answer. I tried following along with another problem and got 2 of them right but am having a hard time on the rest. Someone please help me! (Answers I know are correct are labeled correct next to them) Thank you!!!

The time it takes me to wash the dishes on a randomly selected night is uniformly distributed between 5 minutes and 16 minutes.

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

  

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

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

   1/11 (correct answer)​Correct

c) Which of the following is the correct description of the picture of the probability distribution of X?

  

1. a bell-shaped curve that starts at 5 and ends at 16
2. a rectangle with edges at 5 and 16 (This is the correct answer)

Correct

d) What is the probability that washing dishes tonight will take me between 6 and 13 minutes?  Give your answer as a fraction.

   Incorrect

  Give your answer accurate to three decimal places.

   Incorrect

e) What is the probability that washing dishes tonight will take exactly 6 minutes?

   

Answer 1

a) We're told that the time it takes to wash the dishes is uniformly distributed on some random night. Since we're given a clear definition for the wash time and not which night of the week, the random variable we're dealing with is certainly "the time it takes me to wash dishes on a randomly selected night". Furthermore, your correct answers to b) and c) are clearly discussing the wash time.

d) I will call our random variable (the wash time) X. P(6 < X < 13) is just the area under the rectangle you described in part c) between x=6 and x=13. Since the height is 1/11, P(6 < X < 13) = (1/11) * (13 - 6) = 7/11

e) Assuming our distribution is continuous, the probability that X takes any exact value is 0 (ie, P(X=6) = 0). This is because in any continuous distribution, there are infinitely many possible outcomes (in this case, all real numbers between 6 and 13 - there are a lot of those!). As a result, the probability of exactly 1 of those infinitely many outcomes is 0. Continuous distributions exist to help us quantify the probability of a range of outcomes.