Answer
a) $132$
b) Wrong
Work Step by Step
a) As per the question, the batting average is obtained by dividing the number of hits by the number of at-bats. Therefore, the number of hits would be $$\text{number of hits} = \text{batting average} \cdot \text{number of at-bats}.\tag{1}$$
From the table of Player $A$, for the year $2011$ $$\text{number of hits} = 0.296 * 446 = 132.016\approx 132$$
b) From equation $(1)$ we have $$\text{number of at-bats} = \frac{\text{total number of hits}}{\text{batting average}}.\tag{2}$$ Equation $(2)$ shows that the number of at-bats will increase when:
$1.$ Greater number of hits
$2.$ Smaller batting average
Player $B$ not only has $33$ lesser hits than Player $A$ but also a greater batting average. This would make the number of at-bats of Player $B$ less than that of Player $A$. Hence, the statement made by the friend is wrong.
