2. On any given day, the chance that John shows up late for work is 78%. we deci

Question

2. On any given day, the chance that John shows up late for work is 78%. we decide to observe if John is late or not over the next 25 days. Using the binomial functions: 16 a. Find the probability that he is late exactly 20 times b. Find the probability that he is late at least 20 times. c. Find the probability that he is late at most 18 times. d. Find the probability that he is on-time 2 times. e. Find the probability that John is late between 15-23 times. f. Find the probability that John is late less than 16 times. g. Give the Mean AND Standard Deviation of this distribution

Explanation / Answer

Let X be the number of times he is late

X follows binomial with parameter n = 25 and p = 0.78

(a) P ( X= 20) = 25C20 (0.78) 20 (1- 0.78) 25-20

= 0.1903

(b) P(X>=20) = P(X= 20) + .......+ P (X= 25)

= 0.1903+ 0.1606+ 0.1035+ 0.0479 + 0.0141 + 0.0020 = 0.5184

(C) P (X<=18) = 1- P (X> 18 ) = 1- [ P( X= 19) + .......+ P (X= 25) ] 1- [ 0.1789 + 0.5184] = 0.3027

(d) P (X= 23) = 0.0479

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