Which of the following is(are) true? I. The mean of a population depends on the particular sample chosen. II. The standard devia
tions of two different samples from the same population may be the same. III. Statistical inferences can be used to draw conclusions about the populations based on sample data.
From statement II in the question, it is true that the standard deviations of two different samples from the same population may be the same. The population standard deviation is a fixed value calculated from every individual in the population. A sample standard deviation is calculated from only some of the individuals in a population.
Also from statement III, it is true that statistical inferences can be used to draw conclusions about the populations based on sample data. The mean of a population does not necessarily depends on the particular sample chosen. Therefore statement I is false.
The graph of b(t) = -16t^2 + 5t + 15 is a parabola opening downward. The maximum value of b(t) occurs at the vertex. The t-coordinate of the vertex is t = -5 / (2(-16)) = 5/32 = 0.15625 sec ≈ 0.2 sec.
