As in the class notes, a survey is conducted and tabulated below.BloodType TotalEthnicGroupO A B ABG1 225 250 200 50725G2 800 75 100 251000G3 150 350 125 60685Total1175 675 425135 2410A person from this survey is chosen at random. Answer the questions below. Do not reduce the fractions!!1. P(G1) 2. P(Type A Blood)3. P(Type B Blood � G3)4. P(G1 � Type AB Blood)5. P(Type A or Type O Blood) 1. Data is gathered from a university graduate program. Data is collected from each person applying to the program. Of the 400 male applicants, 100 were accepted. Of the 400 female applicants 60 were accepted.Not accepted Accepted TotalMale 300 100Female 340 60Totala) Determine P(Accepted | Male) b) Determine P(Accepted | Female)c) Comparing the answers in part a and b, do things seem a bit unfair at the university?1. Suppose that it is known that a certain disease occurs in 1% of the population. Suppose also that wehave a certain medical test to determine if person has this disease. The test produces a positive reading on99.4% of those infected with the disease. Suppose that this test gives a positive result in healthy patients2% of the time. Assume we have 100,000 random individuals that follow the above information perfectly. a) Fill in the table.Has Disease Does Not Have Disease TotalTest PositiveTest NegativeTotal100000b) Determine (Have the Disease | Tested Positive)Pc) Determine (Have the Disease | Tested Negative)P 2. Determine the probability that the above circuit will work given the component (works) probabilities.a) ( ) .85 ( ) .71P A P B= = b) ( ) .92 ( ) .98P A P B= =c) ( ) .65 ( ) .84P A P B= =1. Use the pmf to determine the mean of the random variable X.a) x 1 2 3 4 5 6 7 8f (x) .05 .15 .15 .25 .05 .15 .1 .1b) x 2 4 6 8 10 12 14 16f (x) .02 .04 .04 .12 .14 .14 .15 .352. Suppose that our company performs DNA analysis for a law enforcement agency. We currently have 2 machinesthat are essential to performing the analysis. When an analysis is performed, the machine is in use for the entire day.Thus, we can perform at most two DNA analyses per day. Based on past experience, the distribution of analysesneeding to be performed on any given day are as follows:Jobs 0 1 2 3 4 5 or moref(x) .08 .12 .21 .24 .21 .14xxf(x)On days with three or more available jobs to perform, since we cannot perform more than two, the law enforcementagency gives the extra jobs to our competitor. We are considering purchasing a third machine. Each day that the machine is in use, we profit $900. What is theyearly expected value of this new machine? (Assume 365 days per year – no weekends or holidays)a) Determine the expected value per day of the third machine for the entire year.b) Determine the expected value of adding a fourth machine for the entire year.Jobs 0 1 2 3 4 5 or moref(x) .08 .12 .21 .24 .21 .14xxf(x)1. Let X be a random variable with Cumulative Distribution Function (CDF) below. Answer the following probability questions: (First write out what you are looking up in “Big F” notation) – such as(3)FDraw the appropriate picture when required.x1 2 3 4 5 6 7 8 9 10( )F x.02 .09 .15 .41 .51 .66 .73 .97 .98 1.0a) ( 5)P X <b) (6 )P X<c) (3 7)P X� <d) (3 )P X�e) ( 8)P X =f) ( 7)P X �g) (2 9)P X< �1. An insurance company sold 8,000 policies ($100,000 payout value) this year. The probability of death for each person has been determined to be .002. The company charges $225 for each policy. Use the Poisson approximation to determine the following.a) P(The company breaks even)b) P(Profits $200,000 or more) c) P(Loses $300,000 or more)e) What value of lwould be used if the probability of death was .0025?1. A company is asked to manufacture a part to be used in the engine of an automobile. The spec limits are LSL = 64.50 and USL = 65.50. Our process standard deviation for this type of process is .21=s. a) Determine pC.b) What do we have to lower the process standard deviation to so that we have 1.0pC =.c) What do we have to lower the process standard deviation to so that we have 1.25pC =.1. The number of patients requiring a certain type of treatment in a given day well modeled by a Poisson distribution with a mean rate of 6l =. The facility currently has 4 machines that are required for the treatment. Each machine can be used on 2 patients per day. Thus, they can currently handle a maximum of 8 patients per day.a) Determine the probability that they have enough machines to treat all patients on a given day. b) Determine the probability that the facility will have enough machines to treat all patients 3 days in a row.c) What is the probability that there will be 24 or fewer patients over a 3 day period?d) If they buy 1 more machine, what is the new probability that the will have enough machines on a given day?e) How many machines would they need if they wanted the probability that they would have enough machines to treat all patients on a given day to exceed .99? Determine the following: a)( 1.36 .28)P Z- � <-b) (1.19 )P Z<c)( .36 2.18)P Z- � �f) ( 1.65 )P Z- <g) Find the number k so that ( ) .05P Z k< =h) Determine