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Math 203 B, Introduction to Statistics Quiz 4
Tom Linton, Spring 2001, Central College
  1. Assume that the yield per acre for a new variety of corn follows a normal distribution with unknown mean m and standard deviation s = 12 bushels per acre. An agricultural researcher plants thirty-five plots of land (one acre each) with the new variety of corn. The average yield for these thirty-five plots is  = 140 bushels per acre.
    1. Give a 90% confidence interval for m, the mean yield per acre for this variety of corn.

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    2. In everyday language (or some close approximation to everyday language), explain what the interval from part (a) tells you about the mean yield per acre.

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    3. If we calculated a 99% confidence interval for m instead of a 90% confidence interval, would the new interval (the 99% confidence interval) be wider or narrower than the old one? Explain.

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    4. If I wanted the margin of error for the 99% confidence interval to be 0.5 bushels, how large would n have to be?

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  2. Grandma Lumpit makes wonderful chocolate chip cookies, however, her eye sight is fading and not all of her cookies end up with chocolate chips in them (some have zero chocolate chips). In fact, each cookie, independent of all other cookies, has a 0.14 chance of having no chips. You buy a dozen of Grandma Lumpit's chocolate chip cookies (chosen at random from a large supply of cookies). You are interested in probabilities associated with
X =  the number of cookies you get which have no chips.
    The above setting describes a binomial random variable X.

    1. What is a success?

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    2. What are the values of n and p?





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    3. What is the probability that you get 2 cookies with no chips?

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    4. What is the mean number of cookies you receive without chips?



    5. What is the standard deviation of the number of cookies in a dozen that have no chips?

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    6. What is the probability that all 12 of your cookies have chips?

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    7. Using the normal approximation to the binomial, what is the approximate probability that a random sample of 10,000 cookies has more than 1450 cookies with no chips in them?