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CP Statistics Miss Sciandra 8.1 Binomial Distribution Name____________________ Date______Pd_______ A Binomial Distribution results from a data set that meets all of the following requirements: 1. ________________________________________________________________________ ________________________________________________________________________ 2. ________________________________________________________________________ 3. ________________________________________________________________________ 4. _______________________________________________________________________ _______________________________________________________________________ Example 1: Blood type is inherited. If both parents carry genes for the O and A blood types, each child has a probability of 0.25 of getting two O genes and so of having blood type O. The number of O blood types amongst 5 children of these parents is the count, x, of successes in 5 independent observations with the probability of 0.25 of a success on each observation. Does this setting meet the requirements to be a Binomial Probability Distribution? Show all 4 requirements apply. Example 2: Deal 10 cards from a shuffled deck and count the number X of red cards. There are 10 observations, and each gives either a red or black card. Is this a binomial distribution? Show all 4 requirements apply. Finding Binomial Probabilities *Note:______________________________________________________________ 1) Discrete 2) Continuous _____________________________ ___________________________ _____________________________ ___________________________ Where to find: *The inequality symbol counts!* CP Statistics Miss Sciandra 8.1 Binomial Distribution Name____________________ Date______Pd_______ Example 3: An engineer selects an SRS of 10 switches from a large shipment for detailed inspection. Unknown to the engineer, 90% of the switches in the inspection pass to meet the specifications. a) What is the probability that 5 of the 10 switches in the sample pass inspection? b) What is the probability that 8 of the 10 switches in the sample pass inspection? c) What is the probability that 5 or 6 of the switches in the sample pass inspection? d) What is the probability that no more than 1 of the 10 switches in the sample fail inspection? *e) What is the probability that less than 7 switches in the sample fail inspection? Example 4: A 10-question multiple choice exam is given, and each question has five possible answers. Ryan takes this exam and guesses at every question. Use the binomial distribution to find the probability that a) He gets exactly 3 questions correct *c) He gets at least one question correct b) He gets no questions correct *d) He gets at least 9 questions correct Mean, Variance, and Standard Deviation- Binomial Distribution 𝝁= 𝝈𝟐= 𝝈= CP Statistics Miss Sciandra 8.1 Binomial Distribution Name____________________ Date______Pd_______ Example 5: An engineer selects an SRS of 10 switches from a large shipment for detailed inspection. Unknown to the engineer, 90% of the switches in the inspection pass to meet the specifications. a) Find the average amount of switches that pass inspection b) Find the variance and standard deviation of the amount of switches that pass inspection Check For Understanding: 1. An electronics store has a 30% chance of selling a home theatre center to a particular customer. If the store has fifteen customers, what is the probability that the store will make seven sales? 2. Miss Sciandra has twenty students in her class. If each student has a 75% chance of showing up to class, what is the probability that at most eighteen students show up to the next class? 3. The probability that Susan will make a particular car sale is 0.05. If Susan talks to ten customers, what is the probability that she will make no more than 2 sales? 4. Philip has twenty customers that are looking for real estate. The probability that Philip will make a particular sale is 0.20. a)What is the probability that he will make at least one sale? b) find the mean, variance, and standard deviation for the amount of sales
