Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution with A = - 8 and B = 8. (a) Compute P (X < 0). (b) Compute P (-4 < X < 4). (c) Compute P (-5 ≤ X ≤ 7). (d) For k satisfying-8 < k < k + 4 < 8,

a) 1/2 (50%)

b) 1/2 (50%)

c) 3/4 (75%)

d) 3/4 (75%)

Step-by-step explanation:

for a uniform distribution

P (X=x) = x-A / (B-A), for A≤x≤B

then

P (X=x) = (x+8) / 16, for - 8≤x≤8

a) P (X<0) = interval chosen / total interval = (0 - (-8)) / (8 - (-8)) = 1/2 (50%)

b) P (-4
c) P (-5
d) for - 8 < k and k + 4 < 8 → k < 4, then - 8
P (X=k) = P (-8