Question

In the dataset, 282 stores are located in urban areas and the remaining 118 stores are from rural areas. Suppose that we randomly select 25 stores. Let Y be the number of stores located in rural areas among the 25 stores. (Hint: you are required to use Microsoft Excel for this question). Keep all answers to 4 decimal places. i. State the probability distribution for Y, including the parameters. ii. Explain your choice of distribution. iii. What is the probability that there are 8 stores located in rural areas? You are required to indicate the probability statement and the complete Excel function used to answer this question. iv. What is the probability that at least 10 stores are located in urban areas? You are required to state the distribution, indicate the probability statement and the complete Excel function used to answer this question.

Answer 1

i) Y follows hypergeometric probability distribution with parameter n=25 ; k=118 and N=282+118=400

ii)

as selection of stores from sample is without replacement therefore trails are not independent from each other.

therefore we are supposed to use hypergeometric probability distribution

iii) probability that there are 8 stores located in rural areas =hypgeomdist(8,118,25,400)=0.1681

iv)

probability that at least 10 stores are located in urban areas =P(at most 15 are in rural area)

=HYPGEOM.DIST(15,118,25,400,TRUE)=0.9998

v