Refer to the Minerals Engineering (Vol. 46-47, 2013) study of the impact of calcium and gypsum on the flotation properties of silica in water, Exercises 2.23, 2.34 and 2.40. Recall that zeta potential (mV) was determined for each of 50 liquid solutions prepared without calcium/gypsum and for 50 liquid solutions prepared with calcium/gypsum.
a. For solutions prepared without calcium/gypsum, find the z-score for a zeta potential measurement of .
b. For solutions prepared with calcium/gypsum, find the z-score for a zeta potential measurement of .
c. Based on the results, parts a and b, which solution is more likely to have a zeta potential measurement of -9.0? Explain.

Data from Exercise 2.23

A high concentration of calcium and gypsum in water can impact the water quality and limit mineral flotation. In Minerals Engineering (Vol. 46-47, 2013), chemical and materials engineers published a study of the impact of calcium and gypsum on the flotation properties of silica in water. Solutions of deionized water were prepared both with and without calcium/ gypsum, and the level of flotation of silica in the solution was measured using a variable called zeta potential (measured in millivolts, mV). Assume that 50 specimens for each type of liquid solution were prepared and tested for zeta potential. The data (simulated, based on information provided in the journal article) are provided in the table and saved in the SILICA data file.

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SILICA Without calcium/gypsum -47.1 -53.0 -50.8 -54.4 -57.4 -49.2 -51.5 -50.2 -46.4 -49.7 -53.8 -53.8 -53.5 -52.2 -49.9 -51.8 -53.7 -54.8 -54.5 -53.3 -50.6 -52.9 -51.2 -54.5 -49.7 -50.2 -53.2 -52.9 -52.8 -52.1 - 50.2 -50.8 - 56.1 -51.0 -55.6 -50.3 -57.6 -50.1 -54.2 -50.7 -55.7 -55.0 -47.4 -47.5 -52.8 -50.6 -55.6 -53.2 -52.3 -45.7 With calcium/gypsum -9.2 -11.6 -10.6 -8.0 -10.9 - 10.0 -11.0 - 10.7 -13.1 -11.5 -11.3 -9.9 -11.8 – 12.6 -8.9 -13.1 – 10.7 -12.1 -11.2 -10.9 -9.1 -12.1 -6.8 -11.5 --10.4 -11.5 -12.1 -11.3 -10.7 -12.4 -11.5 -11.0 -7.1 -12.4 -11.4 -9.9 -8.6 –13.6 –10.1 -11.3 - 13.0 -11.9 -8.6 -11.3 -13.0 - 12.2 -11.3 -10.5 -8.8 -13.4