A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than 13 centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of 54 bolts. The sample mean bolt length was 13.05 centimeters. The population standard deviation is known to be a = 0.18 centimeters. What is the test statistic z? Ex: 1.23 What is the p-value? Ex. 0.123 Does sufficient evidence exist that the length of bolts is actually greater than the moon unlun pt o pignifionpon loul of 0.01 Select

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X is a discrete random variable with the following PMF: P(X = 1.4) = 0.25 P(X = -9.7) = 0.25 P(X = 10) = 0.5 Find the standard deviation of X.

2. Take a bivariate normal distribution with two random variables X and Y, with mean value = (1, -1), var(X) = 3, var(Y) = 6, and cor(X,Y) = -0.5. %3! (a) create a contour plot for this data (b) plot 1,000 simulations of this distribution (c) Using 1,000,000 simulations, find (1) the expected value of Y (ii) the expected value of Y, given that X> 2 (ii) the expected value of Y, given that X = 2