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AP Statistics 6.3A Assignment 1. Explain whether the given random variable has a binomial distribution. A. Seed Depot advertises that 85% of its flower seeds will germinate (grow). Suppose that the company’s claim is true. Judy buys a packet with 20 flower seeds from Seed Depot and plants them in her garden. Let X = the number of seeds that germinate. B – germinates or not I – each seed is independent of the others N – there are 20 trials S – the probability of success is 0.85 for each seed It is a binomial distribution B. Put the names of all the students in your class in a hat. Mix them up, and draw four names without looking. Let Y = the number whose last names have more than six letters. B – the student’s last name has 6 or more letters or not I – the number of letters in each student’s last name is independent of the other student’s last name N – there are 4 trials S – the probability of success is not the same for each trial It is not a binomial distribution C. Exactly 10% of the students in a school are left-handed. Select students at random from the school, one at a time, until you find one who is left-handed. Let V = the number of students chosen. B – the student is left handed or not I – whether or not a student is left handed is independent of the other student’s left handedness N – there is not a set number of trials It is not a binomial distribution 2. Suppose you purchase a bundle of 10 bare-root rhubarb plants. The sales clerk tells you that on average you can expect 5% of the plants to die before producing any rhubarb. Assume that the bundle is a random sample of plants. Let Y = the number of plants that die before producing any rhubarb. A. Use the binomial probability formula to find P(Y = 1). Interpret this result in context. 10 1 9 P Y 1 0.05 0.95 0.3151 1 B. Would you be surprised if 3 or more of the plants in the bundle die before producing any rhubarb: Calculate an appropriate probability to support your answer. P Y 3 1 P Y 2 1 P Y 2 P Y 1 P Y 0 10 10 10 2 8 1 9 0 10 1 0.05 0.95 0.05 0.95 0.05 0.95 0.0115 1 0 2 I would be surprised because the probability that 3 or more plants in the bundle would die by chance is about 1%. 3. Seed Depot advertises that 85% of its flower seeds will germinate (grow). Suppose that the company’s claim is true. Judy buys a packet with 20 flower seeds from Seed Depot and plants them in her garden. Let X = the number of seeds that germinate. A. Find the probability that exactly 17 seeds germinate. Show your work. 20 17 3 P X 17 0.85 0.15 0.2428 17 B. If only 12 seeds actually germinate, should Judy be suspicious that the company’s claim is not true? Compute P(X < 12) and use this result to support your answer. P X 12 P X 12 P X 11 ... P X 0 20 20 20 12 8 11 9 0 20 0.85 0.15 0.85 0.15 ... 0.85 0.15 0.0059 12 11 0 I would be surprised because the probability that 12 or less of the seeds would germinate by chance is about ½ %.

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