Suppose X is a normal random variable with mean u = 17.5 and o = 6. A random sample of size n = 24 is selected from this population. a. Find the distribution of b. Find P(X < 14) and P(X < 14) Find P(15

Let X1, X2, .., X,, be a random sample from a distribution with mean µ and variance o2. Consider the random variable, X.Which of the following •..., properties are true? Select all that apply. On average, the sample mean is equal to the population mean. The variance of the sample mean is equal to the population variance divided by n. For any n, the distribution of the sample mean depends on the distribution of the population mean. For any n, the sample mean is exactly normally distributed. For n sufficiently large, the sample mean is exactly normally distributed. For any n, the sample mean is approximately normally distributed. For n sufficiently large, the sample mean is approximately normally distributed. For n sufficiently large, the distribution of the sample mean depends on the distribution of the population mean.

Assume that the sample is a random sample from a distribution that is reasonably normally distributed and that we are doing inference for a population mean.  find the are in a t-distribution to the left of -0.68 if the sample has size n=20

Let y1, .., Yn be a simple random sample of size n from UTM students. Assume that the population size is N. Suppose that y; equals 1 (if the participant is COVID-19 fully vaccinated) or 0 (if the participant is not COVID-19 fully vaccinated). Let p be the population proportion and q = 1– p. Define p =-E{-1Yi and ĝ = 1 – p. Some useful facts: E(y:) = p, V(y;) = pg. You may use any needed fact about expected value/variance from previous courses such as STA256H5 without proof. Also, well-known facts from STA304H5 maybe used directly without proof. Only describe what you are doing. If sampling is with replacement, find V (p). Show all steps. If sampling is with replacement, show that is unbiased estimator of п-1 V (p). Show all steps. If sampling is without replacement, find E(). Show all steps. Simplify bd your answer.