please answer this

True or False. Write TRUE if the statement is unconditionally true. Otherwise, write FALSE. (1 pt each) 1. As the degrees of freedom increases, the probability density function of the Student's t-distribution approaches the standard normal distribution. 2. The Central Limit Theorem states that the sample mean of a random sample is approximately normally distributed, if the random sample came from a large population with finite mean and variance and the sample size is sufficiently large. 3. Xia=0.10,v=20,) = -X(a=0.90,v=20)'Problem Solving. Solve the following problems. Show all pertinent solutions. No immediate rounding. Round off final answers to three decimal places. 1. Find the value of the following: (1 pt each) A. to.025,9 B. to.05,11 C. X6.01,2 D. X6.10,4 2. Suppose (X1, X2, ...,X9) is a random sample from Normal(u = 2,0' = 42). Let X be the sample mean of X1, X2, ...Xg and $2 be the sample variance of X1, X2, ..., X9. For items asking for the distribution of a statistic, do not forget to specify the parameters. (1 pt each) A. What is the distribution of X? B. What is the distribution of 8-2? C. What is the distribution of x-27 D. What is the standard error of X? 3. Suppose a company repacks cereal with the use of a machine that is calibrated so that the weight of cereal dispensed in a box is normally distributed with mean 0.40 kg and variance 0.01 kg , although the weight stated in the cereal box is 0.45 kg. For quality control purposes, suppose a random sample of 15 cereal boxes is taken. What is the probability of selecting a random sample with mean weight less than the advertised weight? (2 pts) The time spent studying (in hours) for the final exam by students in a certain university has unknown mean & and standard deviation 8 hours. A random sample of 4 students was taken to guess the mean study time of all students in the university. What is the (approximate) probability that the sample mean X differs from the population mean y by less than 4 hours? That is, approximate P(1X - ul