Question

6. Williams Freight is a national trucking company. The number of physical damage claims to Williams Freight trucks in a given year is normally distributed with a mean of 200 and a standard deviation of 20. Based on these parameters, perform the following calculations. (use the "Areas Under a Normal Curve" table distributed in class or on the last page of your midterm exam) a. What is the probability in a given year that fewer than 230 physical damage claims will occur? (1.5 points) b. What is the probability in a given year that between 185 and 215 physical damage claims will occur? (1.5 points) c. Above what number of physical damage claims do the highest 10 percent of all physical damage claims in a given year fall? (1 point)

Answer 1

Answer: For Calculation we use the formula:

Z = (X-Mean)/Standard Deviation

Solution is given below:

Meanu - 2.00 o = 20 (a) = 230 2-X-4 230-200 z = 1.5 2.32 Pal2:15 09 0.9332 (from 2 table) Xe=25- XL 4X2 is 200 2.1) 2.- Mac, 185200+0.75 at = -0.75 0.2266 P, = 0.5-0.2266= 0.2734 at 2:0.75 0.2734 P=P, f/2 = 0.2734 +0.2734 = 0.5468 (P = 0.5468 (C) at highest loy of damage P=0.90 from 2 table we find that boo.go at 2=1.28 Therefore, 1.28= X-200 x-200= 256 X = 225.60 Above 225.60 10% of damage claims tall.