34 percent of the undergraduate students in a large university have full-time jobs. A random sample of 26 undergraduate students are selected. What is the variance of the number of students who have full-time jobs in such a sample? Calculate to two decimal places(Hint: This is a binomial experiment)
To calculate the variance of the number of students who have full-time jobs in a random sample, we need to use the formula for the variance of a binomial distribution.
The variance of a binomial distribution is given by the formula:
Variance = n * p * (1 - p)
where:
- n is the number of trials or sample size
- p is the probability of success on each trial
In this case, the sample size is 26 (as specified in the question), and the probability of success (having a full-time job) is 34% or 0.34 (as specified in the question).
Using these values, we can calculate the variance:
Variance = 26 * 0.34 * (1 - 0.34)
Variance = 26 * 0.34 * 0.66
Variance = 5.44
Therefore, the variance of the number of students who have full-time jobs in a random sample of 26 undergraduate students is 5.44 (rounded to two decimal places).