9. Eighty students in a school cafeteria were asked if they favored a ban on smo

Question

9. Eighty students in a school cafeteria were asked if they favored a ban on smoking in the cafeteria The results of the survey are shown in the table Class Freshman Favor Oppose No opinion 15 27 If a student is selected at random, find these probabilities. (a) The student is a freshman. (b) The student is a freshman and favors the ban. (c) The student is a freshman or favors the ban. (d) Given that the student favors the ban, the student is a sophomore. (e) The student has no opinion about the ban, given that the student is a freshman 10. The age distribution of employees for this college is shown below Age Under 20 20-29 30 39 40-49 50 and over 10 #of employees 25 48 32 15 If an employee is selected at random,find the probabity that he or she is in the following age groups. (a) Between 30 and 39 years of age (b) Under 20 or over 49 years of age 11. A recent study of young executives showed that 30 percent run, 20 percent bike and 12 percent do both. What is the percent of young executives who run or bike? 12. A survey of publishing jobs indicates that 92% are completed on time. Assume that three jobs are selected for study (a) What is the probability they are all completed on time? (b) What is the probability that at least one was not completed on time?

Explanation / Answer

9:

Following table shows the row total and column total:

(a)

Out of 80 students, 50 are freshman so the required probability is,

P(freshman) = 50 /80 = 0.625

(b)

Out of 80 students, 15 are freshman and favors the ban so the required probability is,

P(freshman and favor) = 15/80 = 0.1875

(c)

Out of 80 students, 15 are freshman or favors the ban so the required probability is,

P(freshman or favor) = P(freshman) + P(favor) - P(freshman and favor) = (50+38-15) / 80 = 0.9125

(d)

Out of 38 favor students, 23 are sophomore is,

P(sophomore | favor) = 23 /80 = 0.2875

(e)

P(no opinion | freshman) = 8 /50 = 0.1600

Class Favor Oppose No opinion Total Freshman 15 27 8 50 Sophomore 23 5 2 30 Total 38 32 10 80

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