Today we discussed instances where the binomial distribution could be transformed into the Normal Curve (because the Normal Curve is more accurate). This can happen if the number of trials (n) times the probability (p) is greater than 10. In other words:
np >= 10 for us to use the normal curve.
To solve, we must recall that the average of a binomial distribution is np, and the standard deviation of a normal distribution is the square root of np(1-p). If we're using the Normal curve, then we must use a z-score (because we use z-scores with Normal Curves). Remember that the formula for a z-score is:
z = x-bar - mu/std. dev.
Calculate the mean (although you already should have, to check the assumption for Normal Curve) and the standard deviation, then plug it into the formula to get your z-score. Once you have your z-score, plug this into Normalcdf(z-score) and that will give you your probability!
Don't forget that we would do 1 - Normalcdf(z-score) if we wanted the top half of the curve.
The example that we did at the end of class today was: Suppose that there is a 5% chance that Mr. Guyton stops you in the hallway. If Amber surveys 300 students, what is the probability that less than 16 of them will have been stopped by Mr. Guyton?
For a video solution to this, please click here:
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