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. 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 ) 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?

Step-by-step explanation:

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

= 0.1293+0.4901=0.6194

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.