Historically, 9 percent of a mail-order firm\'s repeat charge-account customers

Question

Historically, 9 percent of a mail-order firm's repeat charge-account customers have an incorrect current address in the firm's computer database. The number of customers out of 16 who have an incorrect address in the database is a binomial random variable with n = 16 and formula36.mml = 0.09. (a) What is the probability that none of the next 16 repeat customers who call will have an incorrect address? (Round your answer to 4 decimal places.) Probability (b) What is the probability that five customers who call will have an incorrect address? (Round your answer to 4 decimal places.) Probability (c) What is the probability that six customers who call will have an incorrect address? (Round your answer to 4 decimal places.) Probability (d) What is the probability that fewer than seven customers who call will have an incorrect address? (Round your answer to 4 decimal places.) Probability

Explanation / Answer

Answer:

Percentage of incorrect address in the database = 9% = 0.09

Probability of incorrect address = 0.09, Probability of correct address = 1-0.09 = 0.91

No. of customers out of 16 who have incorrect address: binomial random variable with n = 16

a. Probability that none of the next 16 repeat customers will have an incorrect address:

Formula for combination nCr = n!/(r! . (n-r)!)

= 16C0*(0.09)0(0.91)16 = [16!/(0!*(16-0!)]*1*(0.91)16 = 1*1*(0.91)16 = 0.2211

b. Probability that five customers who call will have an incorrect address:

= 16C5*(0.09)5(0.91)11 = [16!/(5!*(16-5!)]*(0.09)5*(0.91)11 = 4368*0.00000590*0.3543 = 0.00914

c. Probability that six customers will have an incorrect address:

= 16C6*(0.09)6(0.91)10 = [16!/(6!*(16-6!)]*(0.09)6*(0.91)10 = 8008*0.00000053*0.3894 = 0.000904

d. Probability that fewer than seven customers who call will have an incorrect address:

This can be solved by binomial cumulative density function with area under the curve P(0 <=X<=7)

= Binomcdf(16,0.09,6) = 0.9980

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