Problem 3: First-generation College Students (no data set)

On February 24^th, 2020, George Mason University Board of Visitors announced that Dr. Gregory Washington was selected as the university's eighth president.In a Washington Post article, Dr. Washington mentioned that he was a first-generation college student.It is known that 39% of George Mason students are the first in their families to attend college.A random sample of ten STAT 250 students were asked the question, "Are you a first-generation college student?"

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.You may use Data Compute Expression and choose the function dbinom.This method relies on you entering all the values of the random variable in the first column of your data table.The other way for 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 = 10.You may present this table horizontally or vertically and leave the probabilities unrounded.

c)Calculate the probability that exactly four of the students in this sample are first-generation college students using the StatCrunch binomial calculator.Copy this image with values from StatCrunch into your document.Then, once you obtain your answer, write one sentence to interpret the probability in context of the question.

d)Calculate the probability that at least two students in this sample are first-generation college students using the probability distribution table you created in 3(b).Show your work "by hand." Then, verify your answer using the StatCrunch binomial calculator.

e)Calculate the probability that between four and seven (inclusive) of the students in this sample are first-generation college students the StatCrunch binomial calculator graph and include this image with values in your document.

f)What is the average number of students you expect to respond "yes" to being a first-generation student? To answer this question, calculate the mean and standard deviation of this probability distribution.Show your work using the binomial mean and binomial standard deviation formulas and provide your answers in your document.Round to two decimal place when necessary. (It is not necessary to use StatCrunch for this part).

g)Imagine you repeated this sample of ten students 10,000 times.We can simulate this in StatCrunch.First, go to Data Simulate Binomial.Next, enter 10,000 for Rows, 1 for Columns, 10 for n, 0.39 for p, and click compute.Then, to visualize these data, go to Graph Bar Plot With Data.Produce a properly titled and labeled relative frequency bar plot and paste it into your solutions.

h)Compare the height of the bar above four with your answer to part (c) and identify which type of probability each value is.