Final answer:
Jack's mean test score will increase by approximately 1.46 if he scores a 90 on his next test. However, this result does not match any of the answer options provided, suggesting a possible error in the question or provided options.
Step-by-step explanation:
The question asks how much Jack's mean test score will increase if he scores a 90 on his next test, given his last six scores. The first step is to find the current mean of his last six scores: (75 + 78 + 83 + 80 + 79 + 84) / 6 = 479 / 6 ≈ 79.83. If Jack scores a 90 on his next test, the new mean will be (75 + 78 + 83 + 80 + 79 + 84 + 90) / 7 = 569 / 7 ≈ 81.29. Therefore, the increase in mean test score is 81.29 - 79.83 ≈ 1.46.
However, on reviewing the question details and the options provided (a-d), it appears there may be an error either in the calculations or in the question itself, as none of the answer options match the calculated increase in the mean test score. It's essential that we use the correct formulas and computations to determine the increase in the mean test score. The formulas and examples given do not directly correspond to this particular question but can illustrate how we might predict scores based on patterns or statistical models, which isn't necessary in this case as we're simply calculating an average.