Despite all the safety instructions they have received, many drivers do not activate their turn signals before changing lanes on the highway leading to accidents and even fatalities. Historical data shows that about 18% of drivers fail to signal before changing lanes. A traffic safety officer observed 135 cars changing lanes on I-66 over the course of his shift. a) What is the probability that more than 35 drivers will fail to activate their turn signal before changing lanes? b) What is the standard deviation of the number drivers who do not activate their turn signals before changing lanes? c) What is the probability that between 20 and 35 drivers (both numbers included in the interval) will fail to use their turn signals before changing lanes?
Despite all the safety instructions they have received, many drivers do not activate their turn signals before changing lanes on the highway leading to accidents and even fatalities. Historical data shows that about 18% of drivers fail to signal before changing lanes. A traffic safety officer observed 135 cars changing lanes on I-66 over the course of his shift.
a) What is the
b) What is the standard deviation of the number drivers who do not activate their turn signals before changing lanes?
c) What is the probability that between 20 and 35 drivers (both numbers included in the interval) will fail to use their turn signals before changing lanes?
Given: Population proportion of drivers that fail to signal before changing lanes, P = 0.18
Let X be the number of drivers that fail to signal before changing lanes, then
Sample size, n = 135
Part a: Required probability is
Part b: Standard deviation of the number of drivers who do not activate their turn signals before changing lanes =
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