Question

Lake Mead Elevations Many people in Nevada, Arizona, and California get water and electricity from Lake Mead and Hoover Dam. Shown in Exercise 4 are an x chart (top) and an R chart (bottom) obtained by using the monthly elevations (ft) of Lake Mead at Hoover Dam (based on data from the U.S. Department of the Interior). The control charts are based on the 12 monthly elevations for each of 75 consecutive and recent years. What does the x chart tell us about Lake Mead?

Short answer

The chart indicates that the elevation of lake is decreasing since past few years and the mean elevation for the lake is not stable.

Step-by-step solution

Given information

Refer to exercise 4 for the \(\bar x\)-chart for the years (time) versus the sample mean of elevations for a Lake. The recordings are taken monthly for 75 consecutive years.

Thus, the sample size is 12 (n).

Step 2:Interpret the graph

Refer to the minitab output of the\(\bar x - {\rm{chart}}\),

The three lines show the three values: centerline (mean of sample means), UCL is the upper control limit, and LCL is the lower control limit. The blue markers represent the mean elevation recorded for each year.

Thus,

\(\begin{array}{c}\bar \bar x = 1164.1\;{\rm{ft}}\\UCL = 1169.8\;{\rm{ft}}\\LCL = 1158.5\;{\rm{ft}}\end{array}\)

Discuss the observations from the graph

Following observations are taken from the graph.

1. The values exceed the upper control limit.
2. There has beenlarge decrease in the last few years in the average elevations.

Thus, it can be concluded that the mean is not stable and the lake has constantly decreasing elevations since last few years.