[5] 4. Suppose a population follows an exactly normal distribution with mean p. = 100, standard deviation 0 = 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). For this question, please make use of the following \"Empirical Rule\" statements: 0 About 68% of outcomes fall within one standard deviation of the mean. 0 About 95% of outcomes fall within two standard deviations of the mean. 0 About 99.7% of outcomes fall within three stande deviations of the mean. [1] a) What is the probability that X takes a value greater than or equal to 116? [2] 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. bino- mial, uniform, normal) is appropriate for X , and specify the values of its parameter(s). [2] c) What is the probability that the sample mean, i, for a sample of size 4 is greater than or equal to 116