Question

Use the probability distribution to complete parts (a) and (b) below. The number of school-related extracurricular activities per student Activities 1 2 3 0.061 0.123 0.161 0.176 0.213 0.128 0.084 0.054 Probability (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is (Round to one decimal place as needed.) The variance is (Round to one decimal place as needed.) The standard deviation is. (Round to one decimal place as needed.) (b) Interpret the results. , so the average student is involved in The standard deviation is. so most of the students The mean is г (Round to one decimal place as needed.) hoxor

Answer 1

mean = E(X) = {up(a) - oxo.o6l+ 1x0.123 + 2x0.161 + 3xo. 176+ uxo.213 +0.128 x5 +6x0.084+ 7x0.054 = 3.3 1. Mean = 3.3 wariance = ECx2) - [ECX3] E(+²) = {x² P(x) = 0 + 1²x0.123 + 2² x 0.161+ 3² +0.176 . +42x0.213 + 5 xo.128 +6²40.0sut 770054 = 14.629 2 variance = ju.629 - 3.3 = 3.7 Standard deviation - 53.7 -1.9 The mean is 3.3, so the average student is involved in 3 or 4 activities. The standard deviation is 1.9, so most of the students differ from the mean by no more than about a activities.