Stats. Normal distribution

Example 8 Six hundred rounds are fired from a gun at a horizontal target 50 m long which extends from 950 m to 1000 m in a range from the gun. The trajectories of the rounds all lie in the vertical plane through the gun and the target. It is found that 27 rounds fall short of the target and 69 rounds fall beyond it. Assuming that the range of rounds is normally distributed, find the mean and standard deviation of the range. Estimate the number of rounds falling within 5 m of the centre of the target. Solution: target gun 950 m 50 m Let X denote the range of the gun in meters. Then X ~ N(u,62) where u and o denote the mean and standard deviation. Since 27 out of 600 rounds fired fall short of the target and 69 rounds fall beyond the target