r=y=(280)(3/52)=16.15 r=16 units Answer 3 a)c0=.08-.03=.05 cu=.35-.08=.27 Critical ratio 27 =.84375 .05+.27 From the given distribution,we have: f() F(Q)_ 0 .05 .05 5 .10 .15 10 .10 .25 15 .20 .45 20 .25 .70 <----.84375 25 .15 .85 30 .10 .95 35 .05 1.00 Since the critical ratio falls between 20 and 25 the optimal is Q=25 bagels. b)The answers should be close since the given distribution appears to be close to the normal. c)u=xf(x)=(0)(.05)+(5)(.10)+...+(35)(.05)=18 σ2=∑x2f(x)-u2=402.5-(18)2=78.5 (2321032) 0= .36 =8.86 The z value corresponding to a critical ratio of.84375 is 1.01. Hence, Q*=0z+μ=(8.86)(1.01)+18=26.95~27.r =  = (280)(3/52) = 16.15 r = 16 units Answer 3 a) c0 = .08 - .03 = .05 cu = .35 - .08 = .27 Critical ratio = .27 .05  .27 = .84375 From the given distribution, we have: Q f(Q) F(Q) 0 .05 .05 5 .10 .15 10 .10 .25 15 .20 .45 20 .25 .70  - - - - .84375 25 .15 .85 30 .10 .95 35 .05 1.00 Since the critical ratio falls between 20 and 25 the optimal is Q = 25 bagels. b) The answers should be close since the given distribution appears to be close to the normal. c)  = xf(x) = (0)(.05) + (5)(.10) +...+(35)(.05) = 18 2 = x 2f(x) -  2 = 402.5 - (18) 2 = 78.5  = (2)(32)(1032) .36 = 8.86 The z value corresponding to a critical ratio of .84375 is 1.01. Hence, Q* = z +  = (8.86)(1.01) + 18 = 26.95 ~ 27