probability

Due to the variation of environmental conditions and imperfections in the measurement method, a single measurement will not produce the exact distance d. The scientist takes n measurements of the distance and uses the sample average to estimate the true distance. From past records of these measurements the scientist knows the variance of a single measurement is 4m2. How many measurements should the scientist make so that the chance that his estimate differs by d by more than 0.5 m is at most 0.05?