Normal Distribution

Hi, can anybody help me with this normal distribution?

Plastic bags are manufactured so that the breaking strength of the bag is normally distributed with a mean of 15.6MPa and a standard deviation of 2.3MPa. bags with breaking strength of less than 11.0MPa are rejected

c) Suppose the standard deviation can be reduced without changing the mean. What should the standard deviation be so that only 1% of the bags will be rejected?

You want 1% to be rejected, so that is 0.5% either side, therefore you will have to find Z(0.995) from your stats tables.
Then think of the formula Z=(X-Mean)/SD and how you could use this to solve the question

Sorry I dont get it. So end up my Z(0.995)=(11-15.6)/SD??

Yeah, and then just rearrange to find what SD will be

OMG! I still dont get it! From my Z-Table i couldnt find 0.995..

You use this table from the formula booklet:

Then you go down to 0.99 and then across to 0.005. This gives you the Z value for 0.995, which is 2.5758
Do you see now?


Posted from TSR Mobile

Shouldn't it be z value for 99% > than population, since only bags < 11Mpa are rejected.
And < 11Mpa is 1% of the population data.

Shouldn't it be that
P(X<11)= 0.01?

Then you standardise so P(Z<11-15.6/SD)=0.01
And then use your tables and symmetry to find the value of SD by rearranging

Correct me if I am wrong, but I believe this is the same thing?

Probably, but hey, simplicity is elegance

Of course FYI I have created a thread for S1 here as there were lots of people asking questions about it
AQA S1 Thread: http://www.thestudentroom.co.uk/showthread.php?p=56225825