7.3 Exercise 49

Use the following to answer the next two exercises: 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.

X ~ N(60, 9). Suppose that you form random samples of 25 from this distribution. Let $\bar{X}$ be the random variable of averages. Let ΣX be the random variable of sums. For parts (c) through (f), sketch the graph, shade the region, label and scale the horizontal axis for $\bar{X}$, and find the probability.

1. Sketch the distributions of X and $\bar{X}$ on the same graph.
2. $\bar{X}$ ~ _____(_____, _____)
3. P($\bar{x}$ < 60) = _____
4. Find the 30^th percentile for the mean.
5. P(56 < $\bar{x}$ < 62) = _____
6. P(18 < $\bar{x}$ < 58) = _____
7. Σx ~ _____(_____, _____)
8. Find the minimum value for the upper quartile for the sum.
9. P(1400 < Σx < 1550) = _____