Question
Please do the problem in Microsoft excel and show all the steps please
46. The Rockwell hardness of a metal is determined by 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 70 and standard deviation 3. (Rockwell hardness is measured on a contin- uous scale.) hardness is a. If a specimen is acceptable only if its between 67 and 75, what is the probability that a ran- domly 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? e. If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is indepen- dently determined, what is the expected number of acceptable specimens among the len? d. What is the probability that at most eight of ten inde- pendently selected specimens have a hardness of less than
Explanation / Answer
Mean=70,SD=3
I shall put here the formulas,you can enter them in excel to get the answers
a)P(67<X<75)=NORM.DIST(75,70,3,TRUE)-NORM.DIST(67,70,3,TRUE)=0.7936
b)P(70-c,70+c)=0.95.
Hence 70-c=NORM.INV(0.025,70,3)=64.1201 , Hence c=5.8799
c)Expected Number=10&0.7936=7.936=8 samples