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2 weeks ago
Credit card sales The National Association of Retailers reports that 62% of all purchases are now made by credit card; you think this is true at your store as well. On a typical day you make 20 sales.

a. Explain why your sales can be considered Bernoulli trials.
b. What is the probability that your fourth customer is the first one who uses a credit card?
c. Let X represent the number of customers who use a credit card on a typical day. What is the probability model for X? Specify the model (name and parameters), and tell the mean and standard deviation.
d. What is the probability that on a typical day at least half of your customers use a credit card?
Textbook 

Stats: Modeling the World


Edition: 4th
Authors:
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2 weeks ago
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a. Bernoulli trials have only two possible outcomes (success = credit/failure = other), trials are independent (one transaction does not influence the next transaction), and the probability of success stays constant on every trial (62% of all purchases).
b. P(first credit card on fourth sale) = P(3 other sales, then credit sale) = (0.38)3(0.62) = 0.034
c. Model: Binom(20, 0.62)
    Mean: μ = np = (20)(0.62) = 12.4,
    SD: σ = = = 2.17
d. P(X ≥ 10) = 1 - P(x ≤ 9) = 1 - = 1 - 0.0923 = 0.9077
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