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(1,400 < Σx < 1,550) = _____