Beverly is building a fireplace. She is using handmade decorative 8-inch bricks for the bottom row of the fireplace. Although the bricks are advertised as 8-inch bricks, the actual length of a brick is variable, and the brick lengths are approximately normally distributed with a mean of 8 inches and a standard deviation of 0.2 inches.

Unfortunately, Beverly didn’t buy enough of the 8-inch bricks, and needs to get two more bricks to try to fill the remaining 15.9 inches. The two additional bricks cannot have a combined length of more than 15.9 inches and must fit in the 15.9-inch space with no more than 0.1 inch of space left over.

What is the probability that two randomly selected bricks will allow Beverly to complete the bottom row of the fireplace? Define 

b₁ = length of the first brick

b₂ = length of the second brick.

A variable that is a linear combination of independent variables that have normal distributions also has a normal distribution.)