Customers arrive at a travel agency at a mean rate of 9 per hour. Assuming that the number of arrivals per hour has a Poisson distribution, give the probability that at least two customers arrive in a given hour.

When a customer buys a product at a supermarket, there is a concern about the item being underweight. Suppose there are 20 “one-pound” packages of frozen ground turkey on display and three of them are underweight. A consumer group buys five of the 20 packages at random. What is the probability that at least one of the five is underweight?

A pair of dice is rolled and X is the random variable defined as the absolute value of the difference of the numbers of dots facing up on two dice. What is the expected value of X? What is the variance of X?

77% of youth now have insurance due to the health care law. Let X equal the number of American youth in a random sample of n = 18 with private health insurance. What is the mean of X?  What is the variance of X?

I need detailed help solving this exercise from homework of Calculus I.I do not really understand how to do, please do it step by step, not that long but clear. Thank you!P.S.: Please do not use AI, thanks!---------------------------------------------------------------------------------Part 3: Fill-in-the-Blank Questions

I need detailed help solving this exercise from homework of Calculus I.I do not really understand how to do, please do it step by step, not that long but clear. Thank you!P.S.: Please do not use AI, thanks!---------------------------------------------------------------------------------Part 1: Multiple-Choice Questions, Each Problem with Single Correct Answer

I need detailed help solving this exercise from homework of Calculus I.I do not really understand how to do, please do it step by step, not that long but clear. Thank you!P.S.: Please do not use AI, thanks!---------------------------------------------------------------------------------Part 1: Multiple-Choice Questions, Each Problem with Single Correct Answer

I need detailed help solving this exercise from homework of Calculus I.I do not really understand how to do, please do it step by step, not that long but clear. Thank you!P.S.: Please do not use AI, thanks!---------------------------------------------------------------------------------Part 2: Multiple-Choice Questions with More Than One Correct Answers

Fred needs to choose a password for a certain website. Assume that he will choose an 8-character password, and that the legal characters are the lowercase letters a, b, c, ..., z, the uppercase letters A, B, C, ..., Z, and the numbers 0, 1, . . ., 9. (a) How many possibilities are there if he is required to have at least one lowercase letter in his password? (b) How many possibilities are there if he is required to have at least one lowercase letter and at least one uppercase letter in his password? (c) How many possibilities are there if he is required to have at least one lowercase letter, at least one uppercase letter, and at least one number in his password?