Please see question:

1. Suppose a population follows an exactly normal distribution with mean p: = 100, standard deviation cr = 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 N000, 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. binou mial, uniform, normal) is appropriate for X , and specify the values of its parameter(s). (c) What is the probability that the sample mean, 53', for a sample of size 4 is greater than or 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 are selected at random for the sample, and the sample mean is 5: = 120. Making use of the fact that the population stande deviation is U = 15, use this sample to build a 95% condence interval for the population mean. You may use approximations derived from the Empirical Rule if you wish. (e) Was the true population mean included in your condence interval from part (1)? What is the probability that a 95% condence interval generated from a sample of size n = 16 would not include the value of the true population mean