Question

Dog weights. Adult German shepherd weights are normally distributed with mean of 73 pounds and standard deviation of 10 pounds. (a) The bottom 21% of weights are below what weight? (b) 79% of weights are above what weight? (c) The top 21% of weights are above what weight? (Round answers to one decimal place)

Answer 1

Ans.

a) 64.9

b) 64.9

c) 81.1

(x-u) Since u = 73 and o = 10 we have: z = n N(0,1) o a) P ( x < x1) (x-u) = P (------< (x1-73) (x1-73) --) = P(Z < ------) 10 10 1) From standard normal table: P ( z < zc) = 0.21 imples zc = -0.8064 P ( z < ze) = 0.21 comparing 1) and 2) we get, (x1-73) /10 = zo (x1-73) /10 = -0.8064 x1 = 64.936 (2) (x2-73) (x-u) P ( x > x2) = P (------> b) = P(Z > (x2-73) ------) 10 1) o 10 -0.8064 2) From standard normal table: P ( z > Z) = 0.79 imples zo = P ( z > -0.8064) = 0.79 comparing 1) and 2) we get, (x2-73) /10 = zo (x2-73) /10 = -0.8064 x2 = 64.936

c) (x-u) P ( x > x3) = P (------ > (x3-73) ------) 10 (x3-73) = P (z > ------) 10 1) o -2) From standard normal table: P ( z > zc) = 0.21 imples zo = 0.8064 P ( z > Zc) = 0.21 comparing 1) and 2) we get, (x3-73) /10 = zc (x3-73) /10 = 0.8064 x3 = 81.064