Answer to Question #249368 in Statistics and Probability for Fuad

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