Hi,
I have got following question:

The length of bolts made in factory Z is normally distributed, with a mean length of 0.1630 m and a standard deviation of 0.0084 m. The probability that a randomly selected bolt is between 0.1546 m and 0.1756m long is between:

A) 54% and 61%

B) 68% and 75%
C)75% & 82.

In my opinion it should be between 68% & 82%. Somebody please guide me.

Zulfi.

C) 75% and 82%



Moderators nore : removed white space

 

This is, sadly, a standard GRE type question. You have presented the problem in a confusing manner as there should be five choices (EDIT more than three anyways, but no matter), not three. Additionally, the answer you gave is not one of the three choices you presented. This is a classic Zulfinian twist designed to confuse the helper and do so with mind-numbing efficiency.

Let's say, for the sake of argument, that the question actually reads something like this:

The length of bolts made in factory Z is normally distributed, with a mean length of 0.1630 meters and a standard deviation of 0.0084 meters. The probability that a randomly selected bolt is between 0.1546 meters and 0.1756 meters long is between

a) 54% and 61%
b) 61% and 68%
c) 68% and 75%
d) 75% and 82%
e) 82% and 89%

Your notes include the area under the curve for +/- 1 standard deviation and you are correct that that is 68% (actually 68.27 if I remember correctly).

The smallest possible bolt size is exactly -1 SD units. But, the largest possible bolt size is MORE than the mean + 1 standard deviation. Therefore, you know that the answer has to be MORE than 68%. Now you can eliminate choices a and b.

But which of the remaining three choices is correct?

So, if the largest bolt size is 0.1756, you need to know what that value is in standardized units (standard deviation units if you like). To do that, you need to convert the value to a Z score. Find that formula and convert the value of the largest size bolt to its Z score equivalent. Also do that for the smallest bolt size.

If you can post those Z values, you can move on to figure out the exact probability of the range of values. That is, the area under the curve between those two values. Then, you can with confidence, choose the correct choice.

 

Don't know if @zulfi100 turned the page on this one, but I wanted to clarify what I meant by "This is, sadly, a standard GRE type question."

If you have seen these types of problems, you may recognize the solution along the lines of; Get the Z scores and then go a table. But, the problem (as I wrote it) can actually be solved WITHOUT going to a table or any wrenching calculations at all. That is, with the Z scores alone.

On the one hand, it is somewhat interesting, I suppose, but horribly contrived (not representative)....that is why I said "sadly". I was wondering just exactly what they (the test people) are trying to discriminate between regarding the answer. My thinking now is that maybe they are simply testing for familiarity with the standard normal curve and memorization of certain points on the curve. Assuming that they do not allow Z tables and calculators in standard testing environments, I guess it is reasonable.

It could be posted as a fun Math problem because it is somewhat clever.