Be quick! Avoiding an accident when driving can de-pend on reaction time. That time, measured from the mo-ment the driver first sees the danger until he or she steps on the brake pedal, is thought to follow a Normal modelwith a mean of 1.5 seconds and a standard deviation of0.18 seconds.a) Use the 68–95–99.7 Rule to draw the Normal model.b) Write a few sentences describing driver reaction times.c) What percent of drivers have a reaction time less than1.25 seconds?d) What percent of drivers have reaction times between1.6 and 1.8 seconds?e) What is the interquartile range of reaction times?f) Describe the reaction times of the slowest 1/3 of alldrivers.
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!
pend on reaction time. That time, measured from the mo-
ment the driver first sees the danger until he or she steps
with a mean of 1.5 seconds and a standard deviation of
0.18 seconds.
a) Use the 68–95–99.7 Rule to draw the Normal model.
b) Write a few sentences describing driver reaction times.
c) What percent of drivers have a reaction time less than
1.25 seconds?
d) What percent of drivers have reaction times between
1.6 and 1.8 seconds?
e) What is the
f) Describe the reaction times of the slowest 1/3 of all
drivers.
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