5. Of the people passing through an airport metal detector, 0.5% activate it. Le

Question

5. Of the people passing through an airport metal detector, 0.5% activate it. Let X be the number among a randomly selected group of 500 who activate the detector. (a) Is X a Binomial random variable? If yes, specify all parameters. (b) Among selected group of 500, what is the probability that only one activates the detector? (c) Among selected group of 500, what is the probability that at most five activate the detector? (d) What is the expected number of people activating the detector? (e) Since n is large and p is small, X can be approximated by a Poisson distribution with parameter = np. Find P(X = 1) by using Poisson distribution. Your answer should be very close to part (b)

Explanation / Answer

a) X is a binomial variable with n=500,p=0.005,q=0.995

2)P( at most 1) = P(1) = 0.005*500*0.995^499=0.2049

c)P( at most 5)=P(0,1,2,3,4,5)=0.95839717963

d) Expected number =np= 500*0.005=2.5

e) P(X=1) = e^-2.5 * 2.5^1 =0.2052

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

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