Question

Problem 3: Choosing House Color 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 sentences 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 this. You may use Data  Compute  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 this 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.

Answer 1

a) Yes this situation fits the Binomial setting. We have n= 19 (finite number)

p= probability that a randomly selected house is painted brown = 0.37 (It is independent of the others and the probability remains the same)

b) Let X= no of houses painted brown

X~Binomial(19,0.37) distribution

PDF of X is given as: P(X=x) = 19Cx*0.37^x*0.63^19-x

Where x=0,1,2,....19

So put the different values of x in the PDF above to get the table.

c) P(X=7) = 19C7*0.37^7*0.63^12 = 0.1870