The president of Doerman Distributors, Inc., believes that 30% of the firm\'s or

Question

The president of Doerman Distributors, Inc., believes that 30% of the firm's orders come from first-time customers. A random ample of LO the proportion of first-time customers Orders will be used to estimate a. Assume that the president is correct and p.30. What is the sampling distribution of P for this study? Select b. What is the probability that the sample proportion will be between .20 and .40 (to 4 decimals)? c. What is the probability that the sample proportion will be between .25 and .35 (to 4 decimals)?

Explanation / Answer

(a) Normal distribution

(b) z1 = (0.2 - 0.3)/{0.3 * 0.7/100} = -2.1822 and z2 = (0.4 - 0.3)/{0.3 * 0.7/100) = 2.1822

P(0.2 < p < 0.4) = P(-2.1822 < z < 2.1822) = 0.9709

(c) z1 = (0.25 - 0.3)/{0.3 * 0.7/100} = -1.0911 and z2 = (0.35 - 0.3)/{0.3 * 0.7/100) = 1.0911

P(0.25 < p < 0.35) = P(-1.0911 < z < 1.0911) = 0.7248

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