A university conducted a survey of 379 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank. Complete parts (a) through (d) below. Freshman Sophomore Junior Senior Satisfied 52 52 60 57 Neutral 26 20 20 10 Not satisfied 21 22 11 28 (a) If a survey participant is selected at random, what is the probability that he or she is satisfied with student government? P(satisfied)equals enter your response here (Round to three decimal places as needed.) Part 2 (b) If a survey participant is selected at random, what is the probability that he or she is a junior? P(junior)equals enter your response here (Round to three decimal places as needed.) Part 3 (c) If a survey participant is selected at random, what is the probability that he or she is satisfied and a junior? P(satisfied and junior)equals enter your response here (Round to three decimal places as needed.)
To solve the problems, we first need to summarize the data provided in the table:
| Class Rank | Satisfied | Neutral | Not Satisfied | Total |
|---|---|---|---|---|
| Freshman | 52 | 26 | 21 | 99 |
| Sophomore | 52 | 20 | 22 | 94 |
| Junior | 60 | 20 | 11 | 91 |
| Senior | 57 | 10 | 28 | 95 |
| Total | 221 | 76 | 82 | 379 |
To find the probability that a randomly selected participant is satisfied with student government, we use the formula:
[ P(\text{satisfied}) = \frac{\text{Number of satisfied students}}{\text{Total number of students}} ]
From the table, the total number of satisfied students is:
[ 52 + 52 + 60 + 57 = 221 ]
Thus, the probability is:
[ P(\text{satisfied}) = \frac{221}{379} \approx 0.583 ]
Rounded to three decimal places:
[ P(\text{satisfied}) \approx 0.583 ]
To find the probability that a randomly selected participant is a junior, we use the formula:
[ P(\text{junior}) = \frac{\text{Number of juniors}}{\text{Total number of students}} ]
From the table, the total number of juniors is:
[ 91 ]
Thus, the probability is:
[ P(\text{junior}) = \frac{91}{379} \approx 0.240 ]
Rounded to three decimal places:
[ P(\text{junior}) \approx 0.240 ]
To find the probability that a randomly selected participant is both satisfied and a junior, we use the formula:
[ P(\text{satisfied and junior}) = \frac{\text{Number of satisfied juniors}}{\text{Total number of students}} ]
From the table, the number of satisfied juniors is:
[ 60 ]
Thus, the probability is:
[ P(\text{satisfied and junior}) = \frac{60}{379} \approx 0.158 ]
Rounded to three decimal places:
[ P(\text{satisfied and junior}) \approx 0.158 ]