An engineer wants to measure a voltage $v$. Being aware of random error in each measurement, the engineer takes $n$ measurements and reports the average of the $n$ measurements as the estimated value of $v$. That is, assume that the $i$-th measurement, $Y_i$, is
$Y_i = v + X_i$
where $X_i$ is the error in the $i$-th measurement. Assuming that the $X_i$'s are IID random variables with $E[X_i] = 0$ and $Var[X_i] = 0.0025$ volts$^2$, the engineer reports the average of the measurements as
$M_n = \frac{Y_1 + Y_2 + ... + Y_n}{n}$
Determine the minimum number of measurements the engineer needs to make so that she is 95\% sure that the reported value is within 0.01 volts of the true value of $v$, i.e., find the value of $n$ such that
$P[v - 0.01 \le M_n \le v + 0.01] \ge 0.95$
Round your answer to the nearest integer.
