QUESTION 1 We have a simple random sample X1. ..-,1 from a Normal population with mean & and standard deviation 5. Select from the following, the probability distribution of: X = (/11)(X1+ ...+X11) O N(0,1) O N(0, 2.27) O N(8, 2.27) O N(8, 25) O N(8, 0.21) QUESTION 2 If X1, X2. ..., X16 is a simple random sample from a Normal population with mean 7 and variance 16. Find P(X > 8). (Give answer correct to 2 decimal places). QUESTION 3 If X1, X2. ..., X5o is a simple random sample from a Normal population with mean u and standard deviation &. Find P( | X - H [> 0.33). (Give answer correct to 4 decimal places). QUESTION 4 If X1, X2. .., Xn is a simple random sample from a Normal population with mean u and variance 1. Find the minimum sample size needed to ensure that: P(| X - | | 6.965) QUESTION 7 Use tables of critical points of the t-distributions to answer the following (give answers correct to 3 decimal places). T observes a t-distribution with 1 degress of freedom Find the following P(T 11.4). (Give answer correct to 3 decimal places)