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In southern California, a growing number of individuals
Chapter 3, Problem 105E(choose chapter or problem)
Problem 105E
In southern California, a growing number of individuals pursuing teaching credentials are choosing paid internships over traditional student teaching programs. A group of eight candidates for three local teaching positions consisted of five who had enrolled in paid internships and three who enrolled in traditional student teaching programs. All eight candidates appear to be equally qualified, so three are randomly selected to fill the open positions. Let Y be the number of internship trained candidates who are hired.
a Does Y have a binomial or hypergeometric distribution? Why?
b Find the probability that two or more internship trained candidates are hired.
c What are the mean and standard deviation of Y ?
Questions & Answers
QUESTION:
Problem 105E
In southern California, a growing number of individuals pursuing teaching credentials are choosing paid internships over traditional student teaching programs. A group of eight candidates for three local teaching positions consisted of five who had enrolled in paid internships and three who enrolled in traditional student teaching programs. All eight candidates appear to be equally qualified, so three are randomly selected to fill the open positions. Let Y be the number of internship trained candidates who are hired.
a Does Y have a binomial or hypergeometric distribution? Why?
b Find the probability that two or more internship trained candidates are hired.
c What are the mean and standard deviation of Y ?
ANSWER:Solution:
Step 1 of 3:
Let Y be the number of internship trained candidates who are hired.
a). Here we need to check whether y has either binomial or hypergeometric distribution.
Given the values are
N be the number of candidates in group = 8
r is who had enrolled in paid internship = 5
N - r = 8 - 5 = 3, is who had enrolled in traditional teaching program.
n is local teaching positions = 3.
The variable y has a hypergeometric distribution. Because the population contains a finite number of elements that have one of two characteristics and a sample is selected from this population.