19 points] Let X = the number of typos per page in the rough draft of a particul

Question

19 points] Let X = the number of typos per page in the rough draft of a particular book. Suppose that X follows a Poisson distribution and that, on average, it has one typo every four pages so that = 0.25. Use the probability mass function to find each of the following. [3 points each (a) Find the chance that a randomly selected page has no typos. (b) Find the chance that a randomly selected page has at most one typo. (c) Suppose that three pages are selected independently of each other. Find the chance that none of them have any typos.

Explanation / Answer

Ans:

Poisson distribution:

mean=0.25 typo per page

a)P(k=0)=e-0.25*(0.250/0!)

=e-0.25

=0.7788

Using Excel funtion:

P(k=0)=POISSON(0,0.25,FALSE)=0.7788

b)P(k<=1)=P(k=0)+P(k=1)

=e-0.25*[(0.250/0!)+(0.251/1!)]

=e-0.25*[1+0.25]

=e-0.25*[1.25]

=0.9735

Using Excel function:

P(k<=1)=POISSON(1,0.25,TRUE)=0.9735

c)Probability that none of three pages have any typo=0.7788*0.7788*0.7788=0.4724

or

e-3*0.25=e-0.75=0.4724

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

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