Ava's morning routine is normally distributed and independent. She has been tracking her time from when she leaves to house to when returns all year. The mean time is 14 minutes and the standard deviation is 1.5 minutes. Suppose two mornings are randomly selected. Find the probability that the first morning selected is more than 2 minutes greater than the second morning time? Interpret this probability.
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!
Ava's morning routine is
Find the probability that the first morning selected is more than 2 minutes greater than the second morning time?
Interpret this probability.
Let X and Y are the first and second mornings.
It is given that X and Y are independent and identically distributed (i.i.d) as normal with mean of 14 minutes and a standard deviation of 1.5.
It is known that the difference of two independent normal random variables is also a normal random variable.
That is, (X–Y) is also a normal random variable.
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