Question

1. Suppose that the algorithm, or robot reporter, typically writes proportion 0.65

of the stories on the site. If 15 new stories are scheduled to appear on a web site next

weekend, find the probability that

a) 11 will be written by the algorithm.

b) at least 10 will be written by the algorithm

c) between 8 and 11 inclusive will be written by the algorithm.

2. The amount of time it takes to assemble a computer is normally distributed, with a mean of 

50 minutes and a standard deviation of 10 minutes. 

a. What is the probability that a computer is assembled in a time between 45 and 60 minutes?

b. What is the probability that a computer is assembled in time more than 65 minutes?

c. What is the probability that their average time will be less than 45 minutes?

Answer 1

Let x-number of stories written by robot. The distribution of the amount of the stories written by computer could be described as Binomial distribution with n = 15 and p = 0.65

1.

(a) $P(x=11) = C \binom{11} {15} * (0.65)^{11}*(0.35)^{4} = 0.1792$

(b) $P(x ⩾ 10 ) = P(x = 10) + ... + P(x=15) = 0.2123+0.1792+0.1110+0.0476 +$

$+0.0126+0.0016 = 0.5643$

(c) $P(8⩽x⩽11) = P(x=8)+P(x=9)+P(x=10)+P(x=11)=0.1319+$

$+0.1906+0.2123+0.1792 = 0.714$

2.

N(50,10) = 50 + 10*N(0,1)

(a) $P(45<50+10*N(0,1) < 60) = P(-0.5<N(0,1)<1)=P(N(0,1)<1)-$

$P(N(0.1)<-0.5)=0.84134-0.30854=0.5328$

(b) $P(50+10*N(0,1)>65) = P(N(0,1)>1.5)=0.06681$

(c) $P(50+10*N(0,1)<45) = P(N(0,1)<-0.5)=0.30854$