Spongebob
There is a multiple choice exam. Only one of five possibilities is correct for each question. There are 60 questions, and you need 19 correct to pass. What is the probability that you pass?
I know the answer is 0.0179, but how do you do it? What function to use? I don't want to use binomial and write out 19 terms...
Answer
Spongebob Squarepants -
Agree, you don't want to add up 19 through 60 terms! So, your text should have explained the Normal Approximation to the Binomial with Continuity Adjustment:
mean = np = 60(1/5) = 12
std. dev. = sqrt[np(1-p)] = 3.098
Now, the continuity adjustment is done because the Normal is "continuous" and Binomial is "discrete". So, instead of using P(X > or equal to 19) we will be using P(X > 18.5) ; look in your text for more detail.
Next, just use the Normal by converting the data to z-values
P(X > or equal to 18.5) = P[z > (18.5 - 12) / 3.098] = P(z > 2.098) = 0.018
Note: Using my TI, the actual Binomial is 0.022. Pretty close! Our approximation would have been even closer if p was closer to 1/2 rather than 1/5.
Hope that helps
Spongebob Squarepants -
Agree, you don't want to add up 19 through 60 terms! So, your text should have explained the Normal Approximation to the Binomial with Continuity Adjustment:
mean = np = 60(1/5) = 12
std. dev. = sqrt[np(1-p)] = 3.098
Now, the continuity adjustment is done because the Normal is "continuous" and Binomial is "discrete". So, instead of using P(X > or equal to 19) we will be using P(X > 18.5) ; look in your text for more detail.
Next, just use the Normal by converting the data to z-values
P(X > or equal to 18.5) = P[z > (18.5 - 12) / 3.098] = P(z > 2.098) = 0.018
Note: Using my TI, the actual Binomial is 0.022. Pretty close! Our approximation would have been even closer if p was closer to 1/2 rather than 1/5.
Hope that helps
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