1. Answer the following questions pertaining to a normally-distributed random variable X.

Suppose the standard deviation of X is 20. Given that 0.2877 of the values of X are greater than 40, what is ? [1 Mark]

Suppose the mean and standard deviation of X are 100 and 30, respectively. Find the numerical value of k such that P(100Xk) = 0.2324. [1 Mark]

Suppose the mean and standard deviation of X are 200 and 50, respectively. Find the numerical value of k where k' and k are equidistant from and P(k' X k) = 0.4714. [1 Mark]

Suppose the mean of X is 82 and P (x <=50) = 0.1660, what is ? [1 Mark]

Suppose the standard deviation of X is 10. Given that 0.5636 of the values of X are greater than 60, what is ? [1 Mark]