Question

Please help me answer this question (discrete distributions).

5-26. A data firm records a large amount of data. Historically, 9% of the pages of data recorded by the firm contain errors If 200 pages of data are randomly selected, a. What is the probability that six or mor b. What is the probability c. What is the probability that none of the pages contain errors? d. What is the probability that fewer than five pages contain errors? e pages contain errors? that more than 10 pages contain errors?

Answer 1

5.26

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We use the binomial distribution to solve the problem. P(X=k out of n total ) = nCx*(p^x)*(1-p)^n-x

p is given out to be .9% or .009

n = 200

a. P(X>=6) = ?

k = 6

P(X>=6)

= 200C6*(.009^6)*(.991^194) +.. +  200C200*(.009^200)*(.991^0)

= .01

b. P(X>=10)

= 200C10*(.009^10)*(.991^190) +.. +  200C200*(.009^200)*(.991^0)

= 0.000017

c. P(X=0) =200C0*(.009^0)*(.991^200) = 0.1639

d. P(X<=5)

= 200C0*(.009^0)*(.991^200) +.. +  200C5*(.009^5)*(.991^195)

= .99