Applied-Probability-and-Statistics Exam Dumps : Applied Probability and Statistics (FZO1 C955)

In a linear regression equation of the form y = mx + b, the slope m gives the predicted change in the response variable y for a one-unit increase in the explanatory variable x. Here, y represents total ice cream sales and x represents average maximum temperature. The equation y = 13x − 598 has slope 13, so the model predicts that ice cream sales increase by about $13 for every 1°F increase in temperature. This is not the sales value at 0°F; that would be the intercept, −598, which is generally not meaningful in this practical context. It is also not the predicted sales at 100°F, because that would require substituting x = 100 into the regression equation. The positive slope matches the upward trend in the scatterplot: higher temperatures are associated with higher ice cream sales. References/topics from the Study Guide: correlation and regression, slope interpretation, explanatory and response variables.

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The sample mean is the standard point estimate for the population mean. A point estimate is a single statistic calculated from sample data and used to estimate an unknown population parameter. If the parameter of interest is the population mean μ, the corresponding sample statistic is x̄. Therefore, the statement is true. This does not mean the sample mean is guaranteed to equal the population mean exactly; sampling variability can cause sample means to differ from the true population mean. However, the sample mean is unbiased under random sampling and becomes more stable as sample size increases. Confidence intervals expand this idea by placing a margin of error around the sample mean. Option B is incorrect because the sample mean is precisely the conventional point estimator for μ. Options C and D impose invalid restrictions. Study Guide references/topics: sample mean, population mean, point estimate, sampling variability.

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When two standard six-sided dice are rolled, there are 6 × 6 = 36 equally likely ordered outcomes. To find the probability that the sum is 7, count all ordered pairs that produce 7. These are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are 6 favorable outcomes. Therefore, the probability is 6/36, which simplifies to 1/6. Since the answer choices include both 6/36 and 1/6, the listed answer from the PDF uses the unsimplified equivalent form, 6/36. Option C, 5/36, omits one valid ordered pair. Option D, 1/12, is too small because it would represent only 3 favorable outcomes out of 36. This problem reinforces that dice outcomes are ordered when two dice are rolled, so (1,6) and (6,1) are counted separately. Study Guide references/topics: sample spaces, dice probability, favorable outcomes, theoretical probability.

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