1. ## Normal distribution Question

A factory manufactures steel poles; the length of the poles are approximately normally dis-
tributed with mean 75cm with standard deviation 1cm. Find the probability that a randomly
selected pole will be between 74.5 and 75.8cm.

Ok What i get when i try to transform this to the standard normal is

Z = .8 for X 75.8

and -.5 for X 74.5

I dont know what to do from here.

Any help greatly appreciated.

Thanks

2. You should look up in a table how big the chance is that a N(0, 1) distributed number is < 0.8, then take 1 - that to get the risk of falling outside. Then you should do the same thing the check the chanse that a N(0, 1) number is > -0.5. You then add the chances of falling outside. You now get the total risk of falling outside, on any of the sides. Take 1 - that to get the probability that a pole is between 74.5 and 75.8.

Note: Your table may not cover negative numbers (this is most likely). Then realize that the chance of the number being > -0.5 is the same as the chance of the number being < 0.5, because of the symmetry around 0.

3. Hey thanks, I tried to look up in a tables but for 0.8 there were 5 different values in the row.

4. There should be only one value. Are you looking in the right table? Ask someone about how to use it if you are not sure how to use the table.

5. Hi thanks for your reply I have this table Standard Normal Distribution Table I think the previous one i was looking at was incorrect.

so for .8 the area is .2881

and for .5 the area is .1915

so 1 - .2881 = .7119

and to fall outside of -.5 its .1915

Then the answer is 1 - ( .1915 + .7119) = .0966??

This seams too small

6. p(-0.5<Z<0.8) = .2881 + .1915 (using your figures) = 0.4796
I always find it best to draw a quick diagam so see if you need to add or subtract areas.

The table you referred to gives area from z=0 out. Some tables give the area from the left tail. Just be aware of what your table is giving you.

7. Hey thanks so much!! We have never even discussed these tables in class and I had spent ages trying to to the integration without joy until i found out about these online.