What do you mean by "central limit theorem is of no use"
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..
What do you mean by "central limit theorem is of no use"
I don't have emotions and sometimes that makes me very sad.
What have you covered in class that looks exactly like this? Side note, that is a pretty small standard deviation.
I don't have emotions and sometimes that makes me very sad.
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.
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