Recent crime reports indicate that 186 motor vehicle thefts occur each hour in t

Question

Recent crime reports indicate that 186 motor vehicle thefts occur each hour in the United States.Assume that the distribution per hour can be approximated by

a Poisson probability distribution.

a) List all the possible random variable values, from 0 through 300, inclusive.

b) Use EXCEL to find and list the associated probability values.c) Now list the 71 random variable values that have associated probability values that exceed

0.001.

d) What is the probability that during any randomly chosen hour exactly 186 motor vehicle thefts

occur?

e) What is the probability that during any randomly chosen hour less than 186 motor vehicle

thefts occur?

f) What is the probability that during any randomly chosen hour more than 186 motor vehicle

thefts occur?

g) What is the probability that during any randomly chosen hour between 170 and 200 motor

vehicle thefts occur?

Explanation / Answer

Let X be the random variable that motor vehicle thefts occur each hour in the United States.

Here we are given that X follows poisson distribution with parameter 186.

What is the probability that during any randomly chosen hour exactly 186 motor vehicle thefts

occur?

That is here we have to find P(X=186).

EXCEL syntax is,

fx --> Poisson --> ok --> x = 186, mean = 186, cumulative = FALSE --> ok

This will gives us probability value is 0.0292.

What is the probability that during any randomly chosen hour less than 186 motor vehicle

thefts occur?

That is here we have to find P(X < 186).

EXCEL syntax is,

fx --> Poisson --> ok --> x = 186, mean = 186, cumulative =TRUE --> ok

This will gives us probability value is 0.5195.

f) What is the probability that during any randomly chosen hour more than 186 motor vehicle

thefts occur?

That is here we have to find P(X > 186).

P(X > 186) = 1 - P(X<186) = 1-0.5195 = 0.4805

This will gives us probability value is 0.4805.

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.