I have these two question and I know the formulas and answers for both, I'm just not sure WHY they both have different formulas, any help would be really appreciated

1. 6 % of drivers read while driving, if 300 are selected at random find the probability that exactly 25 read, so I would have n=300 p= 0.06 q= o.94 x=25
then I do find the mean (n*p) and SD ( square root of n*p*q ), find the z score and look it up on the z table.


2. A missile guidance system has five fail safe components the probabilty of each failing is 0.05, find the probability that exactly 2 will fail

so here I have n=5 p= 0.05 q=0.95 x=2

The formula for this is p^x * q^n-x * nCr


Why do these have different formulas, Thanks so much for your time.

For 1, looking up the z-score would be useful if you want to know the probability that at least 25 drivers read, or fewer than 25 read, but it won't help tell you the probability that exactly 25 out of the 300 read. For this you need to use the binomial probability formula:



For 2 you are correct, except that the combination you want is nCx - not sure what you meant by the variable 'r.'

Thanks, what I'm asking is what is the difference between the two problems that I'll know which formula to do. I happen to know these two but if I get 2 similar problems on a test I wouldn't know which formula to do. Thanks again I really appreaciate it.

Both problems use the same formula - the binomial probability formula. You use this whenever you want to know the probability of something that has a discreet outcome (either success or failure) happening a precise number of times. In your examples the outcomes are discreet - a driver is either a reader or he's not, and a part is either faulty or it's not.

The z-score approach that you described is useful when you are told that the probability of something is normally distrubuted (which BTW is a good assumption for binomial distribution with large values of n), and you are interested in the probability of a result falling withn a range of possible outcomes. For example if you want the probability that fewer than 25 people in the sample are readers, or the probability that between 30 and 50 people in the sample are readers, then the z-score method can be used to figure the probability of the outcome falling within those ranges. It's also used where outcomes are measured on a continuum rather than being discreet and you are looking for the probability that an individual outcome falls in a given range. For example if you measure the height of a group of individuals you will get a continum of rsults, and you can use the z-score method to find the probability that the height of an individual falls into a particular range of those results, perhaps between 5 feet 8 and 6 feet tall.