A supermarket has a self-service checkout area. The management knows that the self-service checkout area can handle 6 customers per minute without a line of customers forming--waiting to get into the self-service checkout area. If 7 or more customers arrive during any minute, some customers will have to wait in line. The random variable C is the count of customer arrivals at the supermarket's self-service checkout area per minute (between 2 pm and 4 pm on weekdays). From long record-keeping, and given usual conditions at its cashier-assisted checkout lanes during that time period, management knows that the population mean of C is 4 and that C has a Poisson distribution.  Compute the probability that the supermarket will have a line of customers waiting to get into the self-service checkout area at any time between 2 pm and 4 pm on weekdays.

Suppose that 6% of a particular population have a particularly nasty disease. There is a test for the disease that correctly identifies those with the disease 98% of the time. However, the same test gives a false positive 1% of the time. Suppose that a random person from this population is given the test as part of a wellness exam. Give answers in decimal form rounded to 4 decimal places as needed. A. Suppose that a random person comes in for a wellness exam and tests positive for the disease. What is the probability that she actually has the disease? B. Suppose that a person comes in for a wellness exam and tests negative. What is the probability that this person does not have the disease? C. What proportion of the total population will test positive? D. What proportion of the total population will not have the disease and will test negative?

A soda company sells one of its soft drinks in 12 ounce cans. In order to ensure that every can has at least 12 ounces in it, the machines in the factory are set to fill each can with an average of 12.1 ounces of soda. Every week, a quality-control technician tests 10 cans to make sure that the average amount of soda in the cans is still 12.1 ounces. If the conclusion of the test is that the number of ounces of soda in the cans is different from 12.1, the technician will declare that the process is out of control, and the machine will be stopped and calibrated. From previous tests, the technician found that the standard deviation of the number of ounces of soda in the cans is approximately 0.01. The number of ounces of soda in the 10 cans that were tested this week is given below. Assume that the standard deviation from the technician's previous tests is the population standard deviation. Use a TI-83, TI-83 Plus, or TI-84 calculator to test whether filling process is out of control and…

57% of all the town's residents own a dog and 66% own a cat. Of the dog owners 49% also own a cat. If a town resident is chosen at random find: (round to 4 decimal places where possible) a.  P(Own a Dog) =  b.  P(Own a Cat) =  c.  P(Own a Cat and a Dog) =  d.  P(Own a Dog GIVEN Own a Cat) =