The table below shows the number of patients at a community hospital: Outpatient Hospitalized Total Men 60 30 90 Women 55 45 100 Total 115 75 190   (a) Find the probability that a patient is hospitalized GIVEN that the patient is a woman. (b) Find the probability that a patient is a woman GIVEN that the patient is hospitalized.  Be sure to answer both questions. You do not have to reduce (simplify) your answers. Write ONLY your answers in the response box. Show your work which justifies your answers ON YOUR PAPER.    

The table below shows the number of patients at a community hospital: Outpatient Hospitalized Total Men 65 30 95 Women 50 45 95 Total 115 75 190   (a) Find the probability that a patient is hospitalized GIVEN that the patient is a woman. (b) Find the probability that a patient is a woman GIVEN that the patient is hospitalized.  Write ONLY your answers in the response box. Show your work which justifies your answers ON YOUR PAPER.

A research study is conducted to test the effectiveness of a new itching cream. A group of 1000 patients are randomly divided into two groups: group A is given the new medicine while the group B is given a placebo. The patients do not know which group they belong to, and neither do the evaluators/assessors as they interview them about the level of itchiness. What type of research study is this?

A survey asks 10,000 people what their household annual income is. This data is quantitative.

As California implemented the “mandatory mask” policy in Spring 2020, the number of new coronavirus cases started to go down for a few months.  What does this say about the “mandatory mask” policy and its effective in slowing down the coronavirus infection in the state of California?

Find the probability that you will get at least one Tails when you toss 3 coins.

A factory manufactures tens of thousands of screws every day. A quality control person inspects every 100th screw to be sure that the dimensions are correct. What type of sampling is this?

Complete the table below.  Suppose 6% of those who take the COVID-19 test actually have the virus. The test is 90% accurate in identifying those with COVID-19 and those without COVID-19. Out of 1000 people tested, find out how many people will test positive and how many of those are “false positives” (those who test positive but don’t actually have the virus).  Tested Positive Tested Negative Total Actually with COVID-19 [a] [b] 60 Actually without COVID-19 [c] [d] 940 Total [e] [f] 1000 Copy this table on your paper and fill in the blank boxes. Write ONLY your answers in the response box. Show your work which justifies your answers ON YOUR PAPER.

A Jeep Cherokee costs $26,000 while a Ford Explorer costs $33,000. By what percent is the Cherokee cheaper than the Explorer? On your paper, show your work and answer. Write only your answer below, but YOUR ANSWER AND WORK SHOULD BE ON YOUR PAPER. 

The statement “If p, then q” is logically equivalent to the statement “If not p, then not q.”