A lecturer commutes daily from his home to university. The average time taken for a one-trip is 30 minutes, with a standard deviation of 4 minutes. Assume the distribution of time taken of the trips is normally distributed. What is the probability that the time taken for a trip is at least 35 minutes? If the lecturer has class at 8.00 A.M. and he leaves his home at 7.40 A.M. daily, determine the probability that he will be late for the class. If the lecturer leaves his home at 7.55 A.M. and all students will be left the lecture hall after they wait from 8.00 A.M. until 8.10 A.M. what is the probability that he enter the class without students?
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!
A lecturer commutes daily from his home to university. The average time taken for a one-trip is 30 minutes, with a standard deviation of 4 minutes. Assume the distribution of time taken of the trips is
- What is the
probability that the time taken for a trip is at least 35 minutes? - If the lecturer has class at 8.00 A.M. and he leaves his home at 7.40 A.M. daily, determine the probability that he will be late for the class.
- If the lecturer leaves his home at 7.55 A.M. and all students will be left the lecture hall after they wait from 8.00 A.M. until 8.10 A.M. what is the probability that he enter the class without students?
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