5.4 EXERCISES SECTION 5.4 Sampling Distributions and the Central Limit Theorem 269 For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary In Exercises 1–4, a population has a mean m and a standard deviation s. Find the mean and standard deviation of the sampling distribution of sample means with sample size n. 1. m = 150, s = 25, n = 49 2. m = 45, s = 15, n = 100 3. m = 790, s = 48, n = 250 4. m = 1275, s = 6, n = 1000 True or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it as a true statement. 5. As the sample size increases, the mean of the distribution of sample means increases. 6. As the sample size increases, the standard deviation of the distribution of sample means increases. 7. A sampling distribution is normal only when the population is normal. 8. If the sample size is at least 30, then you can use z@scores to determine the probability that a sample mean falls in a given interval of the sampling distribution. Graphical Analysis In Exercises 9 and 10, the graph of a population distribution is shown with its mean and standard deviation. Random samples of size 100 are drawn from the population. Determine which of the figures labeled (a)–(c) would most closely resemble the sampling distribution of sample means. Explain your reasoning. 9. The waiting time (in seconds) to turn left at an intersection 10 0.005 0.010 0.015 0.020 0.025 0.030 0.035 20 Time (in seconds) Relative frequency 30 40 50 σ= 11.9 = 16.5 μ x P(x) (a) 0 10 −10 20 30 40 σ μ x Time (in seconds) x = 16.5 x = 11.9 (b) 0 −2 2 4 6 σ μ x Time (in seconds) x = 1.65 x = 1.19 (c) 10 20 30 40 x Time (in seconds) σ μx = 16.5 x = 1.19
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