Question

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,

Answer 1

a) 1/2 (50%)

b) 1/2 (50%)

c) 3/4 (75%)

d) 3/4 (75%)

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<X<4)= interval chosen / total interval =(4-(-4))/(8-(-8)) = 1/2 (50%)

c) P(-5<X<7)= interval chosen / total interval =(7-(-5))/(8-(-8)) = 3/4 (75%)

d) for −8 < k and k + 4 < 8 → k < 4 , then -8<k<4 , thus k

P(X=k)= P(-8<X<4) = interval chosen / total interval =(4-(-8))/(8-(-8)) = 3/4 (75%)