Explain the following question detaily

You are working with an immortal cell line that is used in labs across the 1world and known to have a mean radius of 5.02pm. with a standard deviation of 0.5Unm. You collect 100 samples, and assume that these are well-modeled as i.i.d. Gaussian random variables. You may nd one or more of the following values useful: . @{-1.3) = (9.11.3) = 0.1 . (bf1.6) = Q(1.6} = 0.05 . tb(2.0) = Q(2.0) = 0.025 (a) What is the variance of the sample mean Var[M1ml? {b) If your sample mean is 5.10am is your sample signicantly different from the baseline model at a signicance level of 095? Justify your approach and support your answer numerically. (c) Say you do not know the true mean (but you still know the true standard deviation is 0.50am]. You observe a sample mean of 5.10am. Construct a condence interval centered around the sample mean with condence level 0.9 for the true mean