Probability questions......help?

Question

a machine cuts rods with a mean length of 0.1m from long metal tubes. a large number of rods are measured accurately and it is found that 95% of them are less than 0.104m in length. assuming that the lengths of the rods re normally distributed calculate the standard deviation of the length(this is a measure of the cutting machine`s accuracy) hence calculate the probability that a rod is cut with a length less than 0.099m

Answer 1

Not enough info to conclude an answer.

Answer 2

I think the number of rods is missing???

Answer 3

Actually, there's plenty of information to find the solution(s).

Two points on the normal curve are identified -- the mean and the 95% point. 45% of the area lies between 0.100 (the mean) and 0.104, so look up the Z score for 0.45 in a standard normal table -- 1.645. Since there are 1.645 standard deviations between 0.100 and 0.104, the standard deviation is (0.104 - 0.100)/1.645 = 0.00243m.

Then, to find the area to the left of 0.99, find the number of standard deviations between (0.099 - 0.100)/0.00243 = -0.4115 = Z. Then find the area associated with Z -- 0.1591.  Since 0.5 of the area is located to the right of the mean, there is 0.1591 + .5 = 0.6591  of the area to the right of 0.099, and thus 0.341 to the left of 0.099, and thus the probability that a rod is cut less than 0.099m is 0.341.