5. (3 points) The General Social Survey asked 1000 people how many hours per day

Question

5. (3 points) The General Social Survey asked 1000 people how many hours per day they were able to relax. Consider these 1000 people to be a population, and let be the number of hours of relaxation for a person at random from this population. The results are presented in the following table. Complete the probability distribution of r. Use three decimal places. Number of Hours 1 Frequency 54 96 166 245 135 85 Probability of Relaxation Time (a) (1 point) Find the probability that a person relaxes at most 3 hours. (b) (1 point) Find the probability that a person relaxes at least 3 hours. (c) (1 point) Find the probability that a person relaxes from 3 to 5 hours. (d) (1 point) Find p (e) (1 point) Find ?. Total Points: 30 Study Guide 12 age 3 of 4

Explanation / Answer

Solution:-

Total = (54+96+166+245+175+185+85+44) = 1050

245/1050

= 0.2333

175/1050 = 0.1667

185/1050

= 0.1762

a. the probability that a person relaxes at most 3 hours = 0.3009  

P(X <= 3) = P(1)+P(2)+P(3)
= 0.0514+0.0914+0.1581
= 0.3009

b. the probability that a person relaxes at least 3 hours = 0.8572

P(X >= 3) = P(3)+P(4)+P(5)+P(6)+P(7)+(8)
= 0.1581+0.2333+0.1667+0.1762+0.081+0.0419
= 0.8572

c. the probaility that a person relaxes from 3 to 5 hours =

= P(3)+P(4)+P(5)
= 0.1581+0.2333+0.1667
= 0.5581

d. ? = ?x*p(x) = 4.4346

e. ? = 1.7517
  

Number of hours 1 2 3 4 5 6 7 8 Frequency 54 96 166 245 175 185 85 44 probability of relaxation time 54/1050 = 0.0514 96/1050 = 0.0914 166/1050 =0.1581

245/1050

= 0.2333

175/1050 = 0.1667

185/1050

= 0.1762

85/1050 = 0.081 44/1050 = 0.0419

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