During the economic downturn caused by the ongoing pandemic, a last semester student goes to career fair booths in a Career Carnival. His/her likelihood of receiving an off-campus interview invitation after a career fair booth visit depends on how well he/she did in BUS201. Specifically, an A in BUS201 results in a probability p = 0.25 of obtaining an invitation, whereas a C Grade in the same course results in a probability of p = 0.05 of an invitation. a. Give the PMF for the random variable Y that denotes the number of career fair booth visits a student must make before his/her first invitation including the visit that results in the invitation. Express your answer in terms of p. b. On average, how many booth visits must a ‘C’ student make before getting an off-campus interview invitation? Find the standard deviation of the number of visits till the first invitation for a ‘C’ student in BUS201. c. Find the probability that an ‘A’ student in BUS201 will need at most 4 booth visits in order to get the first off-campus interview invitation.
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.
During the economic downturn caused by the ongoing pandemic, a last semester student goes to career fair booths in a Career Carnival. His/her likelihood of receiving an off-campus interview invitation after a career fair booth visit depends on how well he/she did in BUS201. Specifically, an A in BUS201 results in a probability p = 0.25 of obtaining an invitation, whereas a C Grade in the same course results in a probability of p = 0.05 of an invitation.
a. Give the PMF for the random variable Y that denotes the number of career fair booth visits a student must make before his/her first invitation including the visit that results in the invitation. Express your answer in terms of p.
b. On average, how many booth visits must a ‘C’ student make before getting an off-campus interview invitation? Find the standard deviation of the number of visits till the first invitation for a ‘C’ student in BUS201.
c. Find the probability that an ‘A’ student in BUS201 will need at most 4 booth visits in order to get the first off-campus interview invitation.
d. Optional: Find the probability that a ‘C’ student in BUS201 will need to visit at least 5 booths to get the first invitation during a typical career fair.
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