Solutions HWA1

8.18: mu = 25, sigma = 2, normal

a: Pr(T >28) = Pr(z > (28-25)/2) = Pr(z > 1.5) = normalcdf(1.5,9999999) = .0668

b: Pr(T < 27) = Pr(z < (27 – 25)/2) = Pr(z < 1) = normalcdf(-9999999,1) = .8413

c: Pr(24 < T < 26) = Pr(-.5 < z < .5) = 2*P(0 < z < .5) = .3829

8.30:

a: Pr(400 <= X < 600) = (C.C.) Pr(399.5 < X < 599.5) = normalcdf(339.5,599.5,491,120) = .5942

(Actual value = (61691+72186+72804+58304)/478193 = 264984/478193 = .5541)

b: Pr(X > 700) = normalcdf(700.5,999999999.5,491,120) = .0404

c: Pr(X = 491) = (C.C.) Pr( 490.5 < X < 491.5) = .0033

d: z_{.75} = .6745. x_{.75} = 491 + (.6745)(120) = 571.939 = 572.

e:

Score (L – R) Freq TheoreticalFreq=normalcdf(L-.5,R+.5,491,120)*478193

200-249 3423 .0145*478193 = 6941.82

250-299 18434 .0332*478193 = 15866.18

300-349 39913 .0639*478193 = 30557.95

350-399 51603 .1037*478193 = 49595.68

400-449 61691 .1419*478193 = 67833.25

450-499 72186 .1635*478193 = 78184.95

500-549 72804 .1588*478193 = 75943.32

550-599 58304 .1300*478193 = 62164.39

600-649 46910 .0897*478193 = 42881.93

650-699 30265 .0521*478193 = 24927.77

700-749 16246 .0256*478193 = 12211.11

750-799 6414 .0105*478193 = 5050.52