A local hospital historical records were kept on the number of times a specific CT scanner was serviced in a given year. Using the information a probability distribution was created letting the random variable x represents the number of times the CT scanner was serviced in a year long period

X= 0 P(X)= .20

X=1 P(X)=.40

X=2 P(X)=.25

x=3 P(X)=.10

x=4 P(X)=.05

NOT THERE HAS NEVER BEEN A YEAR THAT CT SCANNER WAS SERVICED MORE THAN 4 TIMES

a. The probability that over the next year the CT scanner will need to be serviced at least 2 times.

b. Determine the mean and standard deviation of this random variable

c. Given that it costs the hospital $500 each time the Ct Scanner is serviced please determine the average servicing cost the hospital can expect to incur from this scanner over the next year/