Free response · Unit 2, Unit 1 Beta

Seeds that sprout: a binomial claim and an experiment

Q4: Across several units · calculator allowed · 10 points

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The question

Name: ______________________   Date: ____________   Seeds that sprout: a binomial claim and an experiment (10 points)

Diagram

A seed company's claim

A seed company claims that 80% of its tomato seeds sprout (germinate) when planted. A community garden buys a very large shipment of the seeds. A gardener selects 15 seeds at random from the shipment, plants them in identical conditions, and finds that 8 of the 15 seeds sprout (invented data).
8 of 15 seeds sprouted (filled with shoots); 7 did not

  1. (a) Assume the company's claim is true. Define the random variable of interest in context, identify its probability distribution with the values of its parameters, and justify that distribution. [3 points]

  2. (b) Assume the company's claim is true. Calculate the probability that 8 or fewer of the 15 seeds sprout. Show your work. [2 points]

  3. (c) Explain what your answer to part (b) suggests about the company's claim. [2 points]

  4. (d) Calculate and interpret the mean of the random variable in part (a), assuming the claim is true. [1 point]

  5. (e) The gardener wants to know whether a new liquid fertilizer increases the percent of these seeds that sprout. She has 60 seeds and 60 identical small pots. Describe how she could use random assignment to carry out an experiment, in enough detail that another person could follow the procedure, and identify what she should compare at the end. [2 points]