Question 862165
m = mean
s = standard deviation.
x = actual value


z = (x-m) / s


p(z) = area under the normal distribution curve taken from the normal distribution tables.


in your problem:


m = 8
s = 2



for part i, the formula becomes:


x = 10


z = (10-8)/2 = 2/2 = 1


p(z > 1) = .1587


if you look up a z of 1 in the following z-score table, it will tell you that the probability of getting a z-score less than 1 would be equal to .8413.
you would then take 1 - .8413 to get the probability of getting a z-score greater than 1.


<a href = "http://lilt.ilstu.edu/dasacke/eco148/ztable.htm" target = "_blank">http://lilt.ilstu.edu/dasacke/eco148/ztable.htm</a>


that takes care of part i.


part ii is taken care of as follows:


x = 4
z = (4-10)/2 = -6/2 = -3


p(z < -3) = .0013


this means that the percentage of tubes that would have to be replaced is .13%.


in this case you take the probability straight off the table, since you want the probability of less than the z-score which is what this particular table is designed to give you.