1 suppose a population follows an exactly normal distribution with mea

Question

1. Suppose a population follows an exactly normal distribution with mean µ = 100, standard deviation o = 16. If you were to randomly sample one individual from this population, we could model the value of that individual (the outcome) using X ~ N(100, 16). (a) What is the probability that X takes a value greater than or equal to 116? Use geogebra or approximate your solution using the Empirical Rule. (b) Suppose a sample of size n = 4 is collected from this population. This sample's mean is one outcome from a random variable X. State which distribution (e.g. binomial, uniform, normal) is appropriate for X, and specify the values of its parameter(s). What is the probability that the sample mean, ī, for a sample of size 4 is greater thanor equal to 116? Use geogebra or approximate your solution using the Empirical Rule. (d) A second sample is collected from the population. This time, n = 16 individuals areselected at random for the sample, and the sample mean is ī = 120. Making use ofthe fact that the population standard deviation is o =a 95% confidence interval for the population mean.derived from the Empirical Rule if you wish.16, use this sample to buildYou may use approximations (e) Was the true population mean included in your confidence interval from part d)?What is the probability that a 95% confidence interval generated from a sample of size n =16 would not include the value of the true population mean?