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John is an expert horseshoe thrower who only misses 15% of the time. Choose the expression that correctly represents the probability John will miss fewer than 50 times if he throws 400 horseshoes. normalcdf(-E99,50,60,7.14) normalcdf(50,E99,60,7.14) normalpdf(-E99,50,400,7.14) normalpdf(-E99,50,60,7.14) normalcdf(-E99,50,400,7.14)
Are you familiar with binomial probability distributions?
first find the mean and st. dev for a binomial distribution mean = n*p st. dev = sqrt( np (1-p))
well you'll start there and then use a normal distribution to approximate it. What's odd is that they didn't account for the continuity correction factor. Oh well Anyways, we are given n = 400 trials p = 0.15 is the probability of success q = 1-p = 1-0.15 = 0.85 is the probability of failure use these values to compute the mean mu and standard deviation sigma mu = n*p = 400*0.15 = 60 sigma = sqrt(n*p*q) = sqrt(400*0.15*0.85) = 7.14
wow thanks guys, now I can do the rest of these problems now that i have an example!
The binomial distribution can be approximated using a normal distribution with mean mu = 60 and standard deviation sigma = 7.14 (approximate) |dw:1433453286569:dw| the mean determines the center while the standard deviation tells you how spread out things are
so if we are asked what is the probability that John "will miss fewer than 50 times if he throws 400 horseshoes." it's essentially asking "what is the area under the normal distribution curve to the left of 50" |dw:1433453396591:dw|
what expression would you type into the calculator to answer the question "what is the area under the normal distribution curve to the left of 50"
that's what i would go for, but remember all of your answer choices are either "normalpdf" or "normalcdf"
so that's why it seems like they want to use the normal distribution to approximate the binomial distribution