Department of Mathematics and Statistics University of North Carolina-Charlotte

Question

Department of Mathematics and Statistics University of North Carolina-Charlotte Statietics 1220 Tast #it Review The following are the 2005 earning ( in thousand of dollars ) before taxes for six employees of a small company 48 .5 38.40 65.50 22.60 1. 79.80 54.60 Calculate the mean, variance and standard deviation: a). As population points b). As sample points 2. The age distribution of a sample of 5000 persons is bell-shaped witha mean of 40 years and standard deviation of 12 years. a). Determine the approximate percentage of people who are 16 to 64 years old. If P(B)-0.59 and P( B) 0.77 a) Find the joint probability of A and B 4. Consider the given table: Against 45 36 In favor 15 Male Female Find the probability of: b). P( female l against) a). P( malel in favor)

Explanation / Answer

A) for population

mean = ( 48.5 + 38.4 + 65.5 + 22.6 + 79.8 + 54.6) / 6 = 51.57

Variance = ((48.5 - 51.57)^2 + (38.4 - 51.57)^2 + ( 65.5 - 51.57)^2 + (22.6 - 51.57)^2 + ( 79.8 - 51.57)^2 + (54.6 - 51.57)^2)/6 = 337.05

standard deviation = sqrt(337.05) = 18.36

b) For sample

mean = ( 48.5 + 38.4 + 65.5 + 22.6 + 79.8 + 54.6) / 6 = 51.57

Variance = ((48.5 - 51.57)^2 + (38.4 - 51.57)^2 + ( 65.5 - 51.57)^2 + (22.6 - 51.57)^2 + ( 79.8 - 51.57)^2 + (54.6 - 51.57)^2)/5 = 404.46

standard deviation = (404.46) = 20.11

2) P(16 < X < 64) = P((16 - 40)12 < Z < (64 - 40)/12)

                            = P(-2 < Z < 2)

                            = P(Z < 2 ) - P(Z < 2)

                            = 0.9772 - 0.0228 = 0.9544

3) P(A and B) = P(A | B) * P(B)

                       = 0.77 * 0.59 = 0.4543

4) a) P(male | in favor) = P(male and in favor)/P(in favor)

                                     = (15/100)/(19/100) = 15 /19 = 0.79

b) P(female | against) = P(female and against)/P(against)

                                   = (36/100)/(81/100) = (36/81) = 0.44

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