rom the U.S. Census Bureau’s American Community Survey in 2019 it was found that 33.13% of United States residents over the age of 25 had an educational attainment of a bachelor’s degree or higher. In the District of Columbia, the percentage of residents over the age of 25 who had attained a bachelor’s degree or higher was 59.67%. An investigator for the U.S. Census Bureau took a random sample of seven residents from the District of Columbia and asked them their highest educational degree they had obtained. a) Verify that the sample from the District of Columbia satisfies the conditions of the binomial experiment. Write one sentence to check each requirement in context of the investigation. b) Assuming the sample from the District of Columbia is a binomial experiment, build the probability distribution in a single table and include the table in your solutions. You may present this table horizontally or vertically and leave the probabilities unrounded. There are two possible ways to do this: To do this is to use the binomial calculator and calculate the probab
From the U.S. Census Bureau’s American Community Survey in 2019 it was found that 33.13%
of United States residents over the age of 25 had an educational attainment of a bachelor’s
degree or higher. In the District of Columbia, the percentage of residents over the age of 25 who
had attained a bachelor’s degree or higher was 59.67%. An investigator for the U.S. Census
Bureau took a random sample of seven residents from the District of Columbia and asked them
their highest educational degree they had obtained.
a) Verify that the sample from the District of Columbia satisfies the conditions of the
binomial experiment. Write one sentence to check each requirement in context of the
investigation.
b) Assuming the sample from the District of Columbia is a binomial experiment, build the
probability distribution in a single table and include the table in your solutions. You may
present this table horizontally or vertically and leave the probabilities unrounded. There
are two possible ways to do this:
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 = 7. Then create the
table in your solutions based on these results.
c) Calculate the probability that at least five individuals from the District of Columbia in
this sample have attained a bachelor’s degree or higher using the probability distribution
table you created in part (b). Type all of your calculations and use proper probability
notation in your solutions. Round your final answer to four decimal places.
d) Verify your answer to part (c) using the StatCrunch binomial calculator. Copy the full
image into your solutions. Write a one-sentence interpretation of the probability in
context of the question.
e) Assume we take a sample of seven United States residents and this sample has a binomial
distribution. Calculate the probability that at least five residents from the United States in
this sample have attained a bachelor’s degree or higher using the StatCrunch binomial
calculator. Copy the image of the Binomial calculator in your solutions. In addition,
write a one-sentence interpretation of the shape of the probability distribution graph.
f) Compare the probability calculated in part (e) to the probability you calculated in part (d)
in one sentence.
g) Calculate the mean and standard deviation of the number of individuals from the District
of Columbia in this sample who have obtained a bachelor’s degree or higher. Show your
work using the binomial mean and binomial standard deviation formulas in your
solutions. Round your answers to two decimal places.
i) Calculate the proportion of the 100 samples that had at least five District of Columbia
residents having obtained a bachelor’s degree or higher. Round your answer to four
decimal places and show your calculation in your solutions.
j) In one sentence, compare the proportion of the 100 samples having at least five residents
with a bachelor’s degree or higher (calculated in part (i)) with the probability of having at
least five residents with a bachelor’s degree or higher (calculated in parts (c) and (d)). In
your comparison, define each probability as empirical or theoretical.
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