Hello,

The questions are in the photo. The exercise referenced (5.24) is attached as well as a screenshot. Thank you.

For Section 5.5: Justification of the Mean as Best Estimate 5.24. * Suppose you have measured a quantity x six times, as follows. 51, 53, 54, 55, 52, 53.Answer these questions after reading the "Projectile Motion: Hitting a Target" assignment. Be sure to show all of your work so that partial credit can be given. 1. [30%] Problem 5.24 (pp. 158-159) from Taylor, J. R. (1997) An Introduction to Error Analysis. 2nd ed., Sausalito, CA: University Science Books. Use the built-in Excel functions to simplify your calculations. Also, use Appendix A (pp. 286-7 in Taylor) to look up the probability. 2. [30%] Suppose that a projectile is launched with a velocity of vo = 3.49 + 0.02 (m/s) at an angle of 0 =76 +10. After traveling a horizontal distance of x = 0.5 m, what is the uncertainty 8x? Hint: apply Equation 3.13 from the assignment: X 8x - Vo Cose V (cos0)2 (8 vo)2 + (vo sine)2(80)2. (3.13) Remember, the uncertainty of the angle must be expressed in radians to obtain the correct result. 3. [40%] Suppose that the shot described in Exercise 2 lands the center of a hoop of diameter 0.08 m. If 100 shots are fired, how many shots do you expect to land outside the hoop? Hint: Use your result for ox from Exercise 2 and the method that you used in Taylor 5.24 to deter- mine the probability that a shot will land outside the hoop.(a) Assuming these measurements are normally distributed, what should be your best estimates for the true value X and the standard deviation o? (b) Based on these estimates, what is the probability that a seventh measurement would fall outside the range of the first six? (Given that your measurements were rounded to the nearest integer, this probability is that for a result x 50.5 or x > 55.5.)