The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring t
he depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 68 and standard deviation 3. (Rockwell hardness is measured on a continuous scale).(A) If a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness?(B) If the acceptable range of hardness is (70-c, 70+c), for what value of c would 95% of all specimens have acceptable hardness?
Given that the Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point.
Let X be the hardness
X is N(68,3)
This area lies on both sides of the mean. Hence we add the corresponding prob values form table
All of the numbers that are listed in or close to the 300's so if you added a 152 it would be very different from the other numbers. Therefore making 152 an outlier.
Let b represent the amount the boy put in the bank. Then (860-b) represents the amount he lent his parents. His earnings were ... 0.045b + 0.07(860 -b) = 51.95 -0.025b = 51.95 -0.07*860 b = -8.25/-0.025 = 330
