The Central Limit Theorem for Sample Means (Averages) · Exercise 17

The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. The distribution to use for the average cost of gasoline for the 16 gas stations is:
(a) $\bar{X}$ ~ N(4.59, 0.10)
(b) $\bar{X}$ ~ N$\left(\text{4}.\text{59},\frac{0.10}{\sqrt{16}}\right)$
(c) $\bar{X}$ ~ N$\left(\text{4}.\text{59},\frac{16}{0.10}\right)$
(d) $\bar{X}$ ~ N$\left(\text{4}.\text{59},\frac{\sqrt{16}}{0.10}\right)$

OpenStax, Introductory Statistics 2e · §7.1 The Central Limit Theorem for Sample Means (Averages) · Exercise 17