Let z ∼ n (0, 1). for a random vector (x1, . . , xn) where n is a positive integer and x1, . . , xn are real-valued random variables, the expectation of (x1, . . , xn) is the vector of elementwise expectations of each random variable and the covariance matrix of (x1, . . , xn) is the n × n matrix whose (i, j) entry is cov(xi , xj ) for all i, j ∈ {1, . . , n}. find the mean and covariance matrix of (z, 1{z > c}) in terms of φ and φ, the standard gaussian pdf and cdf respectively

3.17 scores on stats final. below are final exam scores of 20 introductory statistics students. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 57, 66, 69, 71, 72, 73, 74, 77, 78, 78, 79, 79, 81, 81, 82, 83, 83, 88, 89, 94 (a) the mean score is 77.7 points. with a standard deviation of 8.44 points. use this information to determine if the scores approximately follow the 68-95-99.7% rule. (b) do these data appear to follow a normal distribution? explain your reasoning using the graphs provided below.