5. A print newspaper \"Banana Daily\" produces one newspaper typescript every da

Question

5. A print newspaper "Banana Daily" produces one newspaper typescript every day. The number of typos in the daily newspaper typescripts is found to be following the Poisson distribution with rate = 10 per day. (a) i. Find the probability that 60 typos found in the typescripts produced in a week. 3 marks] ii. Given that there are 60 typos found in the typescripts produced from Monday to Sunday, find the probability that there were 10 typos found in Monday's 3 marks (b) What is the expected number of typos found in the typescripts produced in January? 3 marks] (c) Determine the expected time until 1000 typos found in the typescripts produced 3 marks] (d) Find the probability that 20 typos were found in the typescripts produced by Day 2, 3 marks] typescript Please specify the unit of time. given that 17 typos found in the typescript produced on Day 1

Explanation / Answer

Question 5

= 10 per day

(a) i. The expected number of Typos produced in one week = 10 * 7 = 70

Here let say that X is the number of typos found in a week

then Pr( X = 60) = POISSON ( X = 60; 70) = 0.0243

ii. Here if there are 60 typos found in the typescript in given week then we have to find the probability of finding 10 typos in Monday's script. So, as the poisson distribution has the memoryless propoerty, it would not affect that this week number of typos on next week monday typos.

Pr(10 erros on monday l 60 typos in the week) = Pr(10 errors on Monday) = POISSON (X = 10; 10) = e-10 1010/10! = 0.1251

(b) Expected number of typos foun in January = 31 * 10 = 310

(c) Here the expected time until 1000 typos would been found = 1000/10 = 100 days

(d) Here the typecript produced on Day 1 doesn't affect the probability that 20 typos wee found in the typescripts by Day 2.

so,

Pr(X = 20 on day 2 l X = 17 on day1 ) = Pr(X = 20 on day 2) = POISSON (X = 20; 10) = 0.0019

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

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