Question 2

2. In a 100 gram bag of pistachios, some shells are too difficult to open by hand. Let X be the number of pistachios in a randomly selected bag that cannot be opened by hand. The probability distribution is given. X 0 1 2 3 4 5 P(x) 0.45 0.275 0.125 0.085 0.05 0.015 STAT/MATH 1F92 Assignment 3 2021-2022 a) Verify this is a valid probability distribution. Explain. b) Find the mean and standard deviation for X, rounded to 1 decimal place, and with applicable units. Show your work. Interpret the mean. c) Find the probability that at least 2 pistachios in a bag cannot be opened by hand. d) Suppose 3 bags of pistachios are selected at random. What is the probability that all 3 bags will have at least 4 pistachios that are too difficult to open by hand? Express your answer with 4 decimal places