stuck with this problem!!!! need help

#1
The minimum force required to break a particular type of cable is normally distributed with mean 12,432 and standard deviation 25. A random sample of 400 cables of this type is selected.
Calculate the probability that at least 349 of the selected cables will not break under a force of 12,400..

PS: central limit theorem is of no use..
 

Dason

Ambassador to the humans
#4
What have you covered in class that looks exactly like this? Side note, that is a pretty small standard deviation.
It's possible they haven't done anything exactly like this. But if you look at it the right way they probably have done two different problems that when connected allow you to get this answer.
 
#5
This problem requires two steps.

First, find the probability that a random cord will snap--> P(X<12400), where X is the minimum force required for a single chord to snap. Find the value of z by doing 12400-12432 / 25, where 12400 is the desired force, 12432 is the mean, and 25 is the standard deviation. Once you get the z value (which is initially negative and needs to be turned positive and subtracted by 1), you see that the probability that X < 12400 is .1003.

Second part of the problem --> finding the probability that 349 of these cables are not under 12400. In other words, finding if 400-349 =51 of these cables are under 12400. This is where you need to use a binomial CDF with n = 400 and p = .1003 because the cable will either snap (success) or not (failure), to determine the probability of the number of cables snapping. Your mean is np = 40.12 and your standard deviation is rad(np(1-p)) = 6.007. Using continuity correction to approximate a binomial CDF under normal assumptions, you do (51.5 - 40.12) / 6.007 to get your z value, where 51.5 is 51 + .5 (continuity correction), 40.12 is the mean, and 6.007 is the SD. Once you get the z value, you see that the probability of this value is ~ .97. That is your answer.