(b) A study of parallel interchange ramps revealed that many drivers do not use
ID: 3368586 • Letter: #
Question
(b) A study of parallel interchange ramps revealed that many drivers do not use the entire length of parallel lanes for acceleration, but seek, as soon as possible, a gap in the major stream of traffic to merge. At one site on Interstate Highway 75, 46% of drivers used less than one third of the lane length available before merging. Suppose we monitor the merging pattern of a random sample of 250 drivers at this site. What is the probability that fewer than 120 of the drivers will use less than one third of the acceleration lane length before merging? (ii)What is the probability that more than 225 of the drivers will use less than one third of the acceleration lane length before merging?Explanation / Answer
To solve this answer easily, we use the function binomcdf(250,0.46,120) and 1-binomcdf(250,0.46,225) on TI-83.
P(X<120) = binomcdf(250,0.46,120) = 0.7164
P(X>225) = 1-binomcdf(250,0.46,225) = 0.0001
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