16) The Thumper Seed Company promises a germination rate of 80% for its arugula

Question

16) The Thumper Seed Company promises a germination rate of 80% for its arugula seeds independent of any other of its arugula seeds. A home gardener has planted 20 of these seeds in seed cups indoors. e) The gardener is going to transplant the seeds that germinate outside. He needs to block off 1 square foot in his garden for every seed that germinates so the plant will have enough space to grow. What is the smallest number of square feet that he can block off so that he is 80% confident that he will have enough space to transplant all the seeds that germinate? f) The gardener wants to be 95% confident that at least 10 seeds will sprout. What is the fewest number of seeds that he could plant to have this confidence?

Explanation / Answer

Solution

Part (e)

Let X = Number of seed that germinate out of 20 seeds. Then, X has a Binomial Distribution with parameter n = 20 and p = 0.8 (we are given 80% of seeds are guaranteed to germinate). We need to find the value of X for which the cumulative probability is 0.8(80% confident of germination). Either using Binomial Distribution Tables or using Excel function, this value can be found. This is found to be 17. So, 17 out of 20 seeds are expected to germinate with 80% confidence. Hence, gardener must block a space 17 sq.ft for the purpose. ANSWER     

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