Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 30 customers per hour or 0.5 customers per minute. Let's assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 45 customers per hour, or 0.75 customers per minute. Determine the following operating characteristics for the system. (Round your answers to four decimal places.) (a) The probability that no customers are in the system 1353 (b) The average number of customers waiting 1786 (c) The average number of customers in the system 1.25 x

In a video game, a specific attack succeeds at a rate of 18% and every try is independent. Determine the probability that the first attack lands on the 2nd or 6th try.

Assume that when adults with smartphones are randomly​ selected, 56​% use them in meetings or classes. If 25 adult smartphone users are randomly​ selected, find the probability that exactly 20 of them use their smartphones in meetings or classes.

Autumn has purchased the insurance policy from an insurance company to cover the value of hers house in case if it gets destroyed due to a fire for the price of $1600 per year. Autumn's house is worth $370000 and the probability that fire destroys the house during the length of the policy is estimated to be 0.4%. Let XX  be the insurance company's profit. Answer the following questions: 1. Create the probability distribution table for XX :  XX  outcome profit xx ,$  P(X=x)P(X=x)    the house is destroyed       the house survived     2. Use the probability distribution table to find the following:  E[X]=μX=E[X]=μX= dollars. (Round the answer to 1 decimal place.)  SD[X]=σX=SD[X]=σX= dollars. (Round the answer to 1 decimal place.)