Question

The number of major faults on a randomly chosen 1 km stretch of highway has a poisson distribution with mean 1.4. the random variable is the distance (in km) between two successive major faults on the highway. part a) what is the probability of having at least one major fault in the next 2 km stretch on the highway? give your answer to 3 decimal places. 0.939 part b) which of the following describes the distribution of , the distance between two successive major faults on the highway? a. b. c. d. e. part c) what is the mean distance (in km) and standard deviation between successive major faults?

a. mean = 0.3571; standard deviation = 0.3571
b. mean = 1.4; standard deviation = 1.4
c. mean = 0.7143; standard deviation = 0.5102
d. mean = 2.8000; standard deviation = 2.8000 e. mean = 0.7143; standard deviation = 0.7143

Answer 1

The probability of having at least one major fault in the next 2 km stretch of highway is 0.939. The distribution of the distance between two successive major faults on the highway is described by the Poisson distribution. The mean distance between successive major faults is 0.7143 km and the standard deviation is 0.3742 km.

Step-by-step explanation:

a. The graph of the distribution of the random variable X, the distance between two successive major faults on the highway, follows a Poisson distribution with mean 1.4. The graph will have a peak at the mean value and will be skewed to the right.

b. The distribution of X, the distance between two successive major faults on the highway, is described by the Poisson distribution.

c. The mean distance between successive major faults is equal to the reciprocal of the mean of the Poisson distribution, which is 1/1.4 = 0.7143 km. The standard deviation of the Poisson distribution is equal to the square root of the mean, which is √1.4 = 0.3742 km.