To avoid unpleasant surprises when the statement comes, you try to record all your credit card transactions in a ledger. Unfortunately, you tend to neglect recording about 5% of your purchases. Suppose that last month, you had 25 purchases on your credit card account. When the statement arrives, you count the number of purchases you forgot to record. The random variable X represents the number of unrecorded transactions in a month with 25 transactions. Explain why this is a binomial experiment. Find and interpret the mean of X. Compute the standard deviation of X. Find the probability that you record all 25 purchases. Find the probability that exactly four purchases would have been unrecorded.
(1) Purchases are independent of each other. It has two possibility either it will be recorded or unrecorded. Probability for unrecorded transaction are same for neglect of all transaction. So it follows binomial distribution.
(II) Mean = 25 * 0.05 =1.25
(III) Standard deviation = 1.08972 (Hint: Sqrt(Variance), Variance = 1.1875)
(IV) P(X=0) = 0.277389 (Hint: 25C0 * 0.05^0 * .95^25)
(V) P(X=4) = 0.0269 (Hint: 25C4 * 0.05^4 * .95^21)
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