MATH 1F92 Lecture 7: Math+1F92-+7.4-+Normal+Approximation+to+the+Binomial+Probability+Distribution+Fill+In
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If you have (cid:370)n(cid:371) number of trials, with two outcomes (success or failure) that are mutually exclusive, and each trial is completely independent of the previous trial, then we have a binomial distribution. The probability of the random variable (cid:370)x(cid:371) having a total of (cid:370)x(cid:371) number of success is equal to: (cid:4666)=(cid:4667)=(cid:4672) (cid:4673)(cid:1868) (cid:4666)(cid:883) (cid:1868)(cid:4667) ) with a mean of: =(cid:1866)(cid:1868) and a standard deviation of:= (cid:1866)(cid:1868) (cid:4666)(cid:883) (cid:1868)(cid:4667) Example: a telemarketer has a 4 hour shift where they usually call about. = (cid:885)(cid:885)(cid:887) (cid:883)(cid:882) (cid:2875)+ (cid:887). (cid:888)(cid:889)(cid:889) (cid:883)(cid:882) (cid:2874) + 0. 000047 + 0. 000258 + 0. 001 + 0. 003. = 0. 0043 or 0. 43: find the probability of more than 5 people staying on the line during that time period. = 0. 9957% or 99. 57: find the probability that more than 32 of the calls stay on the line during that time period. In situations like part c, it will take us forever.