Question

Consider the probability distribution of X, where X is the number of job applications completed

by a college senior through the Career Center before getting a job.
X01234567
P(X) 0.0112= 0.115 3 = 0.123 4=0.144 5=0.189 6=0.238 7=0.178
What is the probability that a randomly selected college senior who uses the career center
completed at least one job application? Report your answer to three decimal places.

Answer 1

The probability distribution of X follows a binomial distribution. The mean of X is 65 and the standard deviation of X is approximately 7.527.

Step-by-step explanation:

The probability distribution of X, the number of households including at least one college graduate, follows a binomial distribution since there are only two outcomes for each household: including at least one college graduate or not. The mean of X can be calculated using the formula: mean = n * p, where n is the number of trials and p is the probability of success. The standard deviation of X can be calculated using the formula: standard deviation = sqrt(n * p * (1 - p)).

For this problem, n = 100 (since 100 households were sampled) and p = 0.65 (since 65% of households include at least one college graduate).

Using the formulas, we can calculate:

Mean = 100 * 0.65 = 65

Standard Deviation = sqrt(100 * 0.65 * (1 - 0.65)) = sqrt(100 * 0.65 * 0.35) ≈ 7.527