On average 320 cars per hour pass a certain point along 42nd

On average, 320 cars per hour pass a certain point along 42nd Avenue between 7 and 8 a.m. on weekdays.

a) what is the average number of cars per minute between 7 and 8am in weekdays?

b) what is the standard deviation for the number of cars per hour and per minute between 7 and 8a.m on weekdays?

c) Because work is planned for the road, the county highway engineer is concerned about traffic congestion. She estimates that, if there more than 3 vehicles per minute than travel speeds will be reduced and congestion occurs. What is the probability that more than 3 vehicles pass the point per minute ?

Solution

a)

320 pass per hour, thus,

320/60 = 5.33333 cars pass per minute. [answer]

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b)

Standard deviation = sqrt(mean) = sqrt(5.333333) = 2.309401005 [answer]

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c)

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    5.333333333      
          
x = our critical value of successes =    3      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   3   ) =    0.221310844
          
Thus, the probability of at least   4   successes is  
          
P(more than   3   ) =    0.778689156 [ANSWER]