In the Western United States there is a saying, "Whisky is for drinken but water is for fighten!" Water and water rights have been fought over ever since ranchers and settlers moved into Wyoming, Nontana, and the West. Even today farmers and ranchers fight cities and large developments over water from snowmelt that originates deep in the Rocky fountains.

A river starts in a massive and beautiful lake. Then it flows through prime trout fishing areas to a famous waterfall. ARer it leaves the park, the river is an Important source of water for wildlife, ranchers, farmers, and cities downstream. How much water does leave the

park each year? The annual flow of the river (unlts 10a cubic meters) is shown here for 19 recent years.

25.9 32.4 33.1 19.1 17.5 24.9 21.0 45.1 30.8 34.3

27.1 29.1 25.6 31.4 23.3 24.1 23.9 25.9 18.6

(a) Is there a *'guaranteed" amount of water farmers, ranchers, and cities wlll get from the river each year?

Yes, flows occur at a constant rate.

Yes, flows average out to the same value across each year.

No, annual flows change at a steady rate from year to year.

No, annual flows are a random variable.

Yes, flows occur at the same rate at corresponding times throughout the year.

(b)What is the "expected" annual flow from the snowmelt? Find the mean, median, and mode. (Round your answers to two decimal places.)

mean median________ mode__________

(c)Find the range and standard deviation of annual flow. (Round your answers to two decimal places.)

range

standard deviation

(d)Find a 75/ Chebyshev interval around the mean. (Round your answers to Mo decimal places.)

Lower Limit

Upper Limit

(e)

Give a five-number summary of annual water f\or from the river. minQ1medianq3max

Make a box-and-whisker plot.

Interpret the five-number summary and the box-and-whisker plot. Where does the middle portion of the data lie?

The middle portion of the data are found to have an annual flow between a lower value of

_____________and a higher value of ___________.

. The total spread of annual flows goes from a lower value of_______________to a higher value of_______________.

What is the interquartile range?

Can you find data outliers? (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f)Another river is a smaller but very important source of water flowing out of the park from a different drainage. Ten recent years of annual water flow data are shown below (units 10a cubic meters).

3.833.814.014.845.815.504.315.814.314.87

Although smaller, is the new river more reliable? Use the coefficient of variation to make an estimate. (Round your answers to Mo decimal place.) original river's coefficient of variation smaller river's coefficient of variation t

What do you conclude?

Neither river is more consistent.

The original river is more consistent.

The smaller river is more consistent.

(g)Based on the data, would it be safe to allocate at least 30 units of the orginal river water each year for agriculturaJ and domestic use? Why or why not?

Yes, Qt is greater than 30 which means over three quarters of the river flows are at or above 30.

No, the median is less than 30 which means more than half the river flows are below 30.

No, Q3 is less than 30 which means more than three quarters of the river Rows are below 30

No, since 30 is an upper outlier it will be very rare to have a flow at or above 30.

Yes, since 30 is an lower outlier it will be very rare to have a flow below 30.