1. A newspaper reported the following numbers of calls per hour received by 911
ID: 3064714 • Letter: 1
Question
1. A newspaper reported the following numbers of calls per hour received by 911 over a specific 36 hour period 2 1349 16 22576422 410 313342 1332 3 25 21 024 The paper also reported the following lengths of time per minute between calls: 29 14 65 8 38 35 4 19 7 14 12 454 27 5 12 50 33 10 15 2 10 1 5 30 41 21 31 118 12 5 24 7 6 3113 2 22 1 30 2 1 3 12 12 9 28 6 50 63 5 17 11 23 2 46 90 13 21 55 43 5 19 47 24 4 6 27 4 6 37 16 41 68 9 5 28 42 3 42 8 52 2 11 41 4 35 21 3 17 10 16 1 68 105 45 23 5 10 12 17 (a) Show graphically that the number of calls per hour have an approximate Poisson distribution with a mean of 3 (b) Show that the sample mean a nd the sample standard deviation of the times between calls are both approximately equal to 20 (c) If X is an exponential random variable with mean 20, compare the probability P(X >15) with the proportion of times that are greater than 15. (d) Compare P(X > 45.51 X> 30.5) with the proportion of observations that satisfy this condition.Explanation / Answer
1)
inter-arrival time between poisson distribution follow exponential distribution
with theta = 1/lambda
2) memoryless property
P(X>15) = P(X > 45.5|X > 30.5)
or in general term
P(X >T) = P(X > x+T|X>x)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.