Answer
15.85%
Work Step by Step
A bell shaped distribution is symmetric. That is, 50% of the length of bolts are greater than 4 inches and 50% of the length of bolts are less than 4 inches.
$4.007−4=0.007=1σ$
So, if 68% of bolts are between $μ−1σ=3.993$ inches and $μ+1σ=4.007$ inches, we can conclude that, $\frac{68}{2}$% $=34$% of bolts are between $μ=4$ inches and $μ+1σ=4.007$ inches.
$4.021−4=0.021=3σ$
So, if 99.7% of bolts are between $μ−3σ=3.979$ inches and $μ+3σ=4.021$ inches, we can conclude that, $\frac{99.7}{2}$% $=49.85$% of bolts are between $μ=4$ inches and $μ+3σ=4.021$ inches.
Now, between 4.007 inches and 4.021 inches: $49.85-34=15.85$%
