A real estate broker was interested in the distribution of house color choices in the state of Virginia. It was
discovered that 37% of houses are painted using the color brown. A random sample of 19 houses was selected from houses located in Virginia.
a) Check if this situation fits the binomial setting. Write four complete sentenu lces addressing each requirement in one sentence each.
b) Assuming this situation is a binomial experiment, build the probability distribution in table form in StatCrunch. There are two ways to do it. You may use Data à Compute à Expression and choose the function dbinom. This method relies on you entering the values of the random variable in the first column of your data table. The other way to do it is is to use the binomial calculator and calculate the probability of each of the values of the random variable from X = 0 to X = 19. You may present this table horizontally or vertically and leave the probabilities unrounded.
c) Calculate the probability that exactly 7 houses in the sample are painted brown using the StatCrunch binomial calculator. Copy this image from StatCrunch into your document. Then, once you obtain your answer, write one sentence to explain what the probability means in context of the question.
d) Calculate the probability that no more than 10 houses are painted brown using the StatCrunch binomial calculator. Again, provide a StatCrunch binomial calculator graph to display your answer. Then, once you obtain your answer, write one sentence to explain what the probability means in context of the question.
e) Calculate the probability that between 6 and 9 houses in the sample (inclusive) are painted brown. Show your work using the probability distribution you built in part (b) to answer this question. Then, verify it with a StatCrunch binomial calculator graph and include this image in your document as well. Finally, once you obtain your answer, write one sentence to explain what the probability means in context of the question.
f) Calculate the mean and standard deviation of this probability distribution. Show your work using the binomial mean and standard deviation formulas and provide your answers in your document. (No need to use StatCrunch for this part).
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