# Binomial Distribution

• BINP

• B = Binary process = 2 process

• I = Independent event

• N = Number of trials

• P = Probability of success

• Binomial Probability

• binompdf(n, p, x)

• n=trials

• p=probability

• x=value • Calculator

• 2ND + VARS (DISTR) • A: binompdf / B: binomcdf • binompdf vs binomcdf  # Practice Questions for Binomial Distribution

• A manufacturer produces a large number of toasters. From past experience, the manufacturer knows that approximately 4% are defective. In a quality control procedure, we randomly select 40 toasters for testing.

• Determine the probability that exactly one of the toasters is defective • Find the probability that at most two of the toasters are defective • Find the probability that more than three toasters are defective # Geometric Distribution

• BINP

• Not given the number of trials
• Question Format

• How many trials until a success
• Geometric Probability

• geometpdf(p,x)

• geometcdf(p,x)

• p=probability of success

• x=number of trials until 1 success # Practice Questions for Geometric Distribution

• There is a probability of 0.09 that a vaccine will cause a certain side effect. Suppose that a number of patients are inoculated with the vaccine. We are interested in the number of patients vaccinated until the first side effect is observed

• Find the probability that exactly 4 patients must be vaccinated in order to observe the first side effect.

![Т1-84 PIus S'tver Editj(n ф TEns [NSTRUMENTS ](./media/image125.png) • What is the probability that the number of patients vaccinated until the first side effect is observed at most 5? # Mean and Standard Deviation 