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C.) Probability of failing = Probability of not passing = P(not getting 60Vo or better)
t\-=@\ \'---/
= I - P(passing)=l-P(x23)= 1 - [0.087891+0.014648 + 0.00097656]= 1-0.L0352
Since "passing and "failing"are complementary events,we can use the rule ofcomplements to find theprobability of failing.P(failing) = 1 - P(passing)= 1 - P(at least 60Vo)= I - P(x > 3). The valueswe use for P(3), P(4), andP(5) are taken from part A.
This is a pretty high likelihood, which means that if the student randomly guesses on this quiz, (s)hewill probably receive a failing grade. Of course, if the student studies and hislher answers are notrandom guesses, (or even if they can narrow the choices down to two instead of four), the probabilityof failing will decrease and the student will have a better chance of passing the quiz.
Just in case you need them, the equations to find mean, standard deviation and variance for a binomial
are quite simple:mean- F-np
standarddeviation= o = ^lrpq
variance= o'=ttpe
Let's try an example that employs these equations.In the game of craps (involving rolling a pair of dice), there is a I/6 chance of rolling a seven. (You mayverify this by using the rules for basic probabilities - see the resource sheet on "Probability.")A.) The dice are rolled 35 times; find the mean and the standard deviation for the number of sevens rolled.B.) Would it be unusual for me to get 12 sevens out of my 35 rolls?
B.) A score is unusual if it is more than 2 standard deviations away from the mean. Find p - 2o and1t + 2o . If 12 is within these two values, it is considered "usual," otherwise, it is "unusual."
p - 20 = 5.8333 - 2(2.2048) = I.42371t + 2o = 5.8333 + 2(2.2048) = 10.2429J
Since 12 is not within 2 standard deviations of themean (12 is not in between I.4237 and 10.2429) weconclude it to be unusual to get 12 sevens out of 35rolls.
4of4
revised 12/19/46
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