Back at Tinker Air Force Base, the specifications for a bolt used in an aircraft MRO application

require that the ultimate tensile strength be at least $18$ kN$.$ It is known that $10\%$ of the bolts

have strengths less than $18\mathrm{.}3$ kN and that $5\%$ of the bolts have strengths greater than $19\mathrm{.}76$ kN$.$

Assume that the uncertain tensile strengths of bolts follow a normal distribution.

a$.$ What proportion of the bolts meet the strength specification?

b$.$ You pick five bolts out of a bin. What is the probability that at least four of them meet

the strength specification