The problem is as shown below:

Question 12 Not yet answered Marked out of 5.00 P Flag question Continuous Random Variables: Question 3.1 The natural logarithm of the hourly wage (in pounds) for women is assumed to be a Gaussian random variable with mean 1.5 and standard deviation 0.5. That is X = log Y ~ N(1.5, 0.5?), where Y is the hourly wage. Note that the moment generating function (mgf) for a Gaussian random variable, with mean / and standard deviation o, is M(t) = exp (ut + olt?/2) and the function (. ) denotes the cumulative distribution function of a standardized (mean 0, variance 1) Gaussian random variable. What is the probability that the logarithm of the hourly wage, X. for a randomly selected woman is less than 1? Select one: O $(3.5) O d(-1) O 1-4(-1.25) O d(-2.5) None of the others Question 13 Not yet answered Marked out of 5.00 Flag question Continuous Random Variables: Question 3.2 Consider the distribution of hourly wages as detailed in Question 3.1. What is the probability that the hourly wage, Y, is greater than 10 pounds per hour (to 2 d.p.)? Select one: 0.74 O 0.95 O 0.35 O 0.48 O None of the othersQuestion 14 Not yet answered Marked out of 5.00 Flag question Continuous Random Variables: Question 3.3 Consider the distribution of hourly wages as detailed in Question 3.1. What is the expected value (to 2 d.p.) of women's hourly wages, E[Y]? Select one: O 5.08 O 8.97 O 12.86 O 10.18 O None of the others Question 15 Not yet answered Marked out of 5.00 P Flag question Continuous Random Variables: Question 3.4 Consider the distribution of wages detailed in Question 3.1 A researcher records the average of the logarithm of wages for a random sample of 64 women. What is the probability (to 2 d.p.) that the average log-wage, X, is greater than 1.6? Select one: O 0.26 O 0.16 O 0.06 O 0.56 O None of the others