DA plant that manufactures 1⁄4 - inch diameter steel bolts can produce thousands of bolts per day. There are strict regulations on the strength of a 1⁄4 -inch blot. The strengths of bolts produced by this plant, when the
machinery is working properly, have a mean of 59.16 (in 1000psi) and a standard deviation of 1.202.
(a) Each day this plant randomly selects 200 bolts from the previous day’s production and records the
strength (in 1000 psi) of each bolt. If the average strength of these 200 bolts is less than 59 (in 1000 psi)
the plant has to check the alignment of the machinery and therefore start production late. Assume that
each day’s production is independent. What is the probability that on any given day (when the
machinery is working properly) the plant will have to start production late?