8. The lengths of steel beams made in a steel = 8.25m and standard deviation = 0
ID: 3336559 • Letter: 8
Question
8. The lengths of steel beams made in a steel = 8.25m and standard deviation = 0.07m. follow a normal distribution with mean (a) A customer requires beams that are no longer than 8.35m. What percentage of the mil's output can be used to supply this customer? (b) It is in the mill's interest to be able to supply 98% of its output to this customer. The mill decides to improve the precision of the production process which alters the standard deviation, what value of should the mill aim for so that it can supply 98% of its output to this customer?Explanation / Answer
= 8.25 = 0.07
X = + z
(a) X = 8.35
Z = (8.35 - 8.25) / 0.07
= 0.1 / 0.07
= 1.4286.
Probability from z table = 0.9234.
(b) Z value for 98% = 2.053.
= (8.35 - 8.25) / 2.053
= 0.0487.