A safety light is designed so that the times between flashes are normally distributed with a mean of 3.50 s and a standard deviation of 0.70 s.     a. Find the probability that an individual time is greater than 4..50 s.         The probability is approximately __________. Round to 4 decimal           places as needed.     b. Find the probability that the mean for 70 randomly selected times is             greater than 4.5 s.         The probability is approximately _______________________.  Round to  4         decimal places as needed.      c.  Given that the light is intended to help people see an​ obstruction,   which result is more relevant for assessing the safety of the​ light?

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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!