A student measures the acceleration \(A\) of a cart moving down an inclined plane by measuring the time \(T\) that it takes the cart to travel \(1 \mathrm{~m}\) and using the formula \(A=2 / T^{2}\). Assume that \(T=0.55 \pm 0.01 \mathrm{~s}\), and that the measurement \(T\) comes from a normal population and is unbiased.

a. Generate an appropriate simulated sample of values \(A^{*}\). Is it reasonable to assume that \(A\) is normally distributed?

b. Use the simulated sample to estimate the standard deviation of \(A\).

c. If appropriate, use the normal curve to find a 95\% confidence interval for the acceleration of the cart.