Suppose > is the standard normal variable. Draw the normal curve for each of the following probability statements to visualize the required area and determine the missing values. Report answers accurate to 2 decimal places. a. P(2 = 0.3483 b. P(2 > = 0.5109 : 0.5 d. P(0 25 = 0.3106 e. P(-2.48 > 0.77) = 0.5689Danny and Nate began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Danny took a test in Art History and earned a 74, and Nate took a test in Social Studies and earned a 68.2. Use the fact that all the students' test grades in the Art History class had a mean of 75.4 and a standard deviation of 12 1, and all the students" test grades in Social Studies had a mean of 63.9 and a standard deviation of 11 to answer the following questions. a) Calculate the z-score for Danny's test grade. b) Calculate the z-score for Nate's test grade. = c) Which person did relatively better? O Nate O They did equally well.A population of values has an unknown distribution with a = 36.5 and a = 75.7. You intend to draw a random sample of size n = $2. What is the mean of the distribution of sample means? (Please enter an exact answer.) What is the standard deviation of the distribution of sample means? = (Please report your answer accurate to 2 decimal places.)