Answer:
a) P(X<100)=0.7855
P(X<200)=0.9418
P(100<X<200)=0.1830
b) P(X>M+2σ)=0.0498
c) Median = 48.74 m
Step-by-step explanation:
If the distance X is modeled by an exponential distribution, with parameter λ=0.01422, we have:
The cumulative probability function can be expressed as:
a) The probability that the distance is at most 100 m is:
The probability that the distance is at most 200 m is:
The probability that the distance is between 100 and 200 m is:
b) The mean is M=1/λ=70.3235 and the standard deviation σ=1/λ=70.3235.
So we have to calculate the probability that X exceeds 2 times the s.d. from the mean:
c) The value of the median distance is