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(e) Compute the mean and standard deviation of the 500 sample means. Are they close to the expected values? These are close to the expected values. X ≈ 100.2 s X ≈ 3.7 (f) Compute the probability that a random sample of 20 people results in a sample mean greater than 108. The Z-score associated with 108 is 108 − 100 z = 16/ √ = 2.24. 20 P(X > 108) = P(Z > 2.24) = 1 − P(Z < 2.24) = 1 − 0.9875 = 0.0125 (g) What proportion of the 500 samples had a sample mean IQ greater than 108? Is this result close to the theoretical value obtained in part (f)? In one simulation 9 sample means were greater than 108. The proportion is thus which is close to the theoretical value. Page 398, Exercise 18 p = 9 = 0.018 500 Cell Phone Only According to a CNN report, 7% of the population do not have traditional phones and instead rely on only cell phones. Suppose a random sample of 750 telephone users is obtained. (a) Describe the sampling distribution of ˆp, the sample proportion that is “cell-phone only.” Since 750(0.07)(1 −0.07) = 48.825 ≥ 10 the distribution is approximately normal with mean of µˆp = 0.07 and a standard deviation of 0.07(1 − 0.07) σˆp = ≈ 0.00931665. 750
(b) In a random sample of 750 telephone users, what is the probability that more than 8% are “cell-phone only”? The Z-score associated with a proportion of 0.08 is Therefore z = 0.08 − 0.07 0.00931665 ≈ 1.07. P(ˆp > 0.08) = P(Z > 1.07) = 1 − P(Z < 1.07) = 1 − 0.8577 = 0.1423. (c) Would it be unusual if a random sample of 750 adults results in 40 or fewer being “cell-phone only”? The sample proportion is ˆp = 40 ≈ 0.053. 750 The Z-score associated with this sample proportion is Therefore z = 0.053 − 0.07 0.00931665 ≈ −1.79. P(ˆp < 0.053) = P(Z < −1.79) = 0.0367. Since this probability is less than 5%, it would be unusual. Page 418, Exercise 30 Billing Process For a certain billing process, the number of days for customers to pay their bill from the date of invoice is approximately normally distributed, with a mean of µ = 47 days and σ = 11 days. A random sample of 10 bills from the billing process during the month of June results in the following data: 55 45 45 42 65 58 35 36 34 60
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Page 5: The sample statistics are The margi

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