1. Population Distribution vs Sampling Distribution

(A) Assume the weight of a single pear follows a normal distribution with a mean of 130 grams and a standard deviation of 18 grams. What is the probability that a randomly selected pear weighs more than 148 grams? Show detailed calculation. Hint: using 68-95-99.7 rule or Table B to find the probability

(B) Now consider the average weight of a sample of 36 pears. What is the sampling distribution of the sample mean weight? Name this distribution and provide its relevant parameter values, such as the mean and standard deviation.

(C) Using the central limit theorem, or your result in (B), calculate the probability that the average weight of a sample of 36 pears will be more than 132 grams. Hint: using a Shiny App or Table B to find the probability.