In a certain store there is a 005 probability that the scann

In a certain store, there is a 0.05 probability that the scanned price in the bar code scanner will not match the advertised price. The cashier scans 886 items.

What is the standard deviation? (Use rounded expected number for the calculation of standard deviation. Round your final answer to 4 decimal places.)

What is the probability of at least 34 mismatches? (Round the value of z to 2 decimals. Use Appendix C-2 to find probabilities. Round your final answer to 4 decimal places.)

What is the probability of more than 52 mismatches? (Round the value of z to 2 decimals. Use Appendix C-2 to find probabilities. Round your final answer to 4 decimal places.)

Solution

(a-1) Expected number= n*p=886*0.05 = 44

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(a-2)standard deviation =sqrt(n*p*(1-p))

=sqrt(886*0.05*0.95)

=6.4873

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(b) The probability is

P(X>=34) = P((X-mean)/s >(34-44)/6.4873)

=P(Z>-1.54) = 0.9382 (from standard normal table)

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(c) The probability is

P(X>52) = P(Z>(52-44)/6.4873)

=P(Z>1.23) =0.1093 (from standard normal table)