One of the important statistics of interest to all 4-year colleges and Universities is student retention rate. It is defined as “the percentage of a school's first-time, first-year undergraduate students who continue at that school the next year”. A very small 4-year college in the Midwest claims to have a retention rate of 85% and admitted 60 Freshmen in Fall 2020. Assuming the claim is true: a. how many freshmen would you expect to continue into their sophomore year in Fall 2021? b. what is the probability that no less than 55 freshmen will continue into their second year in Fall 2021? c. what is the probability that no less than 50 and no more than 55 freshmen will continue into their second year in Fall 2021? d. After doing some research, you find out that this college admitted 70 freshmen in Fall 2019 and 65 of them continued on to their second year in Fall 2020. Are you inclined to believe their 85% retention claim? Justify with appropriate calculations.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
One of the important statistics of interest to all 4-year colleges and Universities is student retention rate. It is defined as “the percentage of a school's first-time, first-year undergraduate students who continue at that school the next year”. A very small 4-year college in the Midwest claims to have a retention rate of 85% and admitted 60 Freshmen in Fall 2020. Assuming the claim is true:
a. how many freshmen would you expect to continue into their sophomore year in Fall 2021?
b. what is the probability that no less than 55 freshmen will continue into their second year in Fall 2021?
c. what is the probability that no less than 50 and no more than 55 freshmen will continue into their second year in Fall 2021?
d. After doing some research, you find out that this college admitted 70 freshmen in Fall 2019 and 65 of them continued on to their second year in Fall 2020. Are you inclined to believe their 85% retention claim? Justify with appropriate calculations.
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