The state department of weights and measures is responsible for making sure that commercial weighing and measuring devices, such as scales, are accurate so customers and businesses are not cheated. periodically, employees of the department go to businesses and test their scales. for example, a dairy bottles milk in 1-gallon containers. suppose that if the filling process is working correctly, the mean volume of all gallon containers is 1.00 gallon with a standard deviation equal to 0.10 gallon. based on this information, if the department employee selects a random sample of n = 9 containers, what is the probability that the mean volume for the sample will be greater than 1.01 gallons?

In a sample of 2023 u. s. adults, 373 said franklin roosevelt was the best president since world war ii. two u. s. adults are selected at random from the population of all u. s. adults without replacement. assuming the sample is representative of all u. s. adults, complete parts (a) through (d). (a) find the probability that both adults say franklin roosevelt was the best president since world war ii. the probability that both adults say franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (b) find the probability that neither adult says franklin roosevelt was the best president since world war ii. the probability that neither adult says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (c) find the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii. the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (d) which of the events can be considered unusual? explain. select all that apply. the event in part left parenthesis a right parenthesis is unusual because its probability is less than or equal to 0.05. the event in part (b) is unusual because its probability is less than or equal to 0.05. none of these events are unusual. the event in part (c) is unusual because its probability is less than or equal to 0.05.