solve using R or R studio

1. The focal length f of an optical instrument is needed. This is determined by using the thin lens formula 1 T2 where r is the distance from the lens to the object and r2 is the distance from the lens to the real image of the object. The distance r is independently measured 12 times and r2 is independently measured 40 times. The mean of the measurements is the actual distances, 9 centimeters and 18 centimeters, respectively. The standard deviation of the measurement is 0.1 centimeters for ri and 0.5 centimeter for r2 (a) Let Ri be the sample mean of the 12 measurements to the object. Estimate, using the central limit theorem, P{R 8.9cm) (b) Let R2 be the sample mean of the 40 measurements to the image. Estimate, using the central limit theorem, P{R 17.9cm) (c) How many measurements are needed so that PR2 18cml > 0.lcm) 0.02. 1. The focal length f of an optical instrument is needed. This is determined by using the thin lens formula 1 T2 where r is the distance from the lens to the object and r2 is the distance from the lens to the real image of the object. The distance r is independently measured 12 times and r2 is independently measured 40 times. The mean of the measurements is the actual distances, 9 centimeters and 18 centimeters, respectively. The standard deviation of the measurement is 0.1 centimeters for ri and 0.5 centimeter for r2 (a) Let Ri be the sample mean of the 12 measurements to the object. Estimate, using the central limit theorem, P{R 8.9cm) (b) Let R2 be the sample mean of the 40 measurements to the image. Estimate, using the central limit theorem, P{R 17.9cm) (c) How many measurements are needed so that PR2 18cml > 0.lcm) 0.02