Question

A random group of thirty customers at a local theater was interviewed regarding their movie viewing habits. The following responses were obtained for the question, "How many times during the past month did you go to the movies?" 1. Number of movies attended 0 1 2 3 4 Number of customers 10 8 6 Construct the probability distribution for X- number of times to attend a movie during the past month and construct the cumulative probability distribution for this data. a. Find the probability that a customer selected at random went to the movies: 1) more than one time, 2) two times, 3) at least two times, 4) no more than three times. b. C. Compute the mean, variance, and standard deviation for this data. According sample, it was found that 35% of young people voted in the last primary election. If three people interviewed, what is the probability that none of them voted in the primary election? Use a tree diagram (decision/contingency tree) to complete this problem. 4. to a recent survey, voter turnout for young people is at an all-time low. From a random are

Answer 1

1 a) Total customers = 3+10+6+8+3 = 30

no. of movies X	No. of customers	Probability of X	Cumulative prob.
0	3	3/30 = 0.1	0.1
1	10	10/30=0.333	0.433
2	6	6/30=0.2	0.633
3	8	8/30=0.266	0.9
4	3	3/30=0.1	1

b) P(X>1) = 1-P(X=1)-P(X=0) = 1-0.433-0.1 =0.567

P(X=2) = 0.2

P(X>=2) = P(X>1) = 0.567

P(X<=3) = 1- P(X=4) = 1-0.1 = 0.9

c)

0.1 00.333 10.2 2+0.266 30.1 41.931 mean Pii

also ,

p 0.102 +0.333* 120.2 22 0.266* 320.1* 425.127 _

so

variance > Pi Pi)2 5.127 -1.9312 1.40 =

Standar ddeviation = variance V1.40 1.18

2) Probability that a young voter voted = 0.35

so among three , probability that none voted = (1-0.35)³ = 0.274625