1 answer

3) A traffic engineer has observed the traffic at a certain intersection between 5 pm and...

Question:

3) A traffic engineer has observed the traffic at a certain intersection between 5 pm and 5:05 pm each day for 100 days. She has tabulated the frequency of the number of cars observed crossing the intersection during this period Number of Number Proportion Cars of Days of Days 36 28 15 10 0.36 0.28 0.15 0.10 0.07 0.04 2 P(x)(0.2)(0.8) P2(x) -(0.4)(0.6)
a) The engineer is trying to obtain a good model for the number of cars using the intersection during this time period. Use pi(x) to compute the probabilities for b) She also consider the model p2(x) as a possibility. Compute the probabilities for c) Compare the results from the two models to the proportion of days in the table. d) Neither model fits the data perfectly. Is this a sufficient reason to reject both the number of cars from 0 to 5 the number of cars in the intersection from 0 to 5 when using this model. Which model provides the better fit do you think? models? Briefly explain your reasoning
3) A traffic engineer has observed the traffic at a certain intersection between 5 pm and 5:05 pm each day for 100 days. She has tabulated the frequency of the number of cars observed crossing the intersection during this period Number of Number Proportion Cars of Days of Days 36 28 15 10 0.36 0.28 0.15 0.10 0.07 0.04 2 P(x)(0.2)(0.8) P2(x) -(0.4)(0.6)
a) The engineer is trying to obtain a good model for the number of cars using the intersection during this time period. Use pi(x) to compute the probabilities for b) She also consider the model p2(x) as a possibility. Compute the probabilities for c) Compare the results from the two models to the proportion of days in the table. d) Neither model fits the data perfectly. Is this a sufficient reason to reject both the number of cars from 0 to 5 the number of cars in the intersection from 0 to 5 when using this model. Which model provides the better fit do you think? models? Briefly explain your reasoning

Answers

a)

number of cars,X no. of days proportion p1(x) = 0.2*0.8^x
0 36 0.36 0.2
1 28 0.28 0.16
2 15 0.15 0.128
3 10 0.1 0.1024
4 7 0.07 0.08192
5 4 0.04 0.065536

b)

number of cars,X no. of days proportion p1(x) = 0.2*0.8^x p2(X)=0.4*0.6^x
0 36 0.36 0.2 0.4
1 28 0.28 0.16 0.24
2 15 0.15 0.128 0.144
3 10 0.1 0.1024 0.0864
4 7 0.07 0.08192 0.05184
5 4 0.04 0.065536 0.031104
total 1 0.737856 0.953344

c)

proportion is high from both model in(x=0,1,2)

model 2 , P2(x) seems somewhat closer to proportions,so it provide better fit than p1(x)

d)

sum of all probabilities should be 1,but here,neither model probability adds to 1.

.

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