The time it takes me to wash the dishes on a randomly selected night is uniformly distributed between 6 minutes and 18 minutes. a) State the random variable in the context of this problem. rv X = a randomly selected night rv X = the time it takes me to wash dishes on a randomly selected night rv X = a uniform distribution rv X = washing dishes Correct b) Compute the height of the uniform distribution. Leave your answer as a fraction. Incorrect c) Which of the following is the correct description of the picture of the probability distribution of X? a bell-shaped curve that starts at 6 and ends at 18 a rectangle with edges at 6 and 18 Correct d) What is the probability that washing dishes tonight will take me between 7 and 17 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 7 minutes?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The time it takes me to wash the dishes on a randomly selected night is uniformly distributed between 6 minutes and 18 minutes.
a) State the random variable in the context of this problem.
rv X = a randomly selected night
rv X = the time it takes me to wash dishes on a randomly selected night
rv X = a uniform distribution
rv X = washing dishes
Correct
b) Compute the height of the uniform distribution.
Leave your answer as a fraction.
Incorrect
c) Which of the following is the correct description of the picture of the probability distribution of X?
a bell-shaped curve that starts at 6 and ends at 18
a rectangle with edges at 6 and 18
Correct
d) What is the probability that washing dishes tonight will take me between 7 and 17 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 7 minutes?
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