
Normal distributions
Hi, I have several problems I would like some help.
PROBLEM 1: Extruded plastic rods are automatically cut into lenghts of 6 inches. Actual lengths are normally distributed about a mean of 6 inches and their standard deviation is 0.06 inch.
1 what proportion of the rods have lenghts that are outside the tolerance limits of 5.9 and 6.1 inches?
Here I did:
p=F((6.16)/0.06) F((5.96)/0.06)= F(1.67)F(1.67)=0.95250.0475=0.905
P(outside tolerance)=10.905=0.095
2 To what value does the standard deviation needs to be reduce if 99% of the rods must be within the tolerance?
I can not fin this question.
PROBLEM 2:
In a photographic process, the developping time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second.
 For which value is the probability 0.95 that it will be exceeded by the time it takes to develop one of the prints?
I dont get this one.
Can I have some help please?