Download 8.1 The Binomial Distributions Objective: Determine if a binomial

8.1 The Binomial Distributions Objective: Determine if a binomial setting is valid Calculate the probability of a binomial distribution Calculate the mean and standard deviation of a binomial setting A family has 3 children. What is the probability that all 3 are girls? We can use a coin to simulate the outcome. A trial consists of flipping the coin once. What are the 2 possible outcomes? H-­‐ T-­‐ Binomial Distribution-­‐ Properties of the Binomial Distribution 1-­‐ 2-­‐ 3-­‐ 4-­‐ Which of the following represents a binomial distribution and why? Ex 1-­‐ Blood type is inherited. If both parents carry genes for the O and A blood types, each child has probability 0.25 of getting two genes and so of having blood type O. Different children inherit independently of each other. Let X represent the number of children with O blood type in 5 independent observations. Ex 2-­‐ Deal 10 cards from a shuffled deck and count the number X of red cards. Complete Ex: 8.1-­‐8.4 Finding Binomial Probabilities Ex: An SRS of 10 switches is taken from a large shipment. 10% of the switches fail to meet specifications. What is the probability that no more than 1 of the 10 switches in the sample fails inspection? Using the calculator: Binompdf(n,p,k) Probability Distribution Function (PDF)-­‐ Cumulative Distribution Function (CDF)-­‐ Binomial Formulas Binomial Coefficient Binomial Probability Ex: The probability of a child having blood type O is 0.25. If 5 children share the same parents, how many ways can 2 of them have blood type O? So what is the probability that exactly 2 of them have blood type O? Ex: What is the probability that no more than 3 of them have blood type O? Mean of a Random Variable µ= Standard Deviation of a Binomial Random Variable σ= Ex: What is the mean and standard deviation of the binomial distribution for the bad switches. Recall n=10 and p=0.1?