The speed with which utility companies can resolve problems is very important. G

Question

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown the cases. Suppose the 35 cases reported today are representative of all complaints. (a-1) How many of the problems would you expect to be resolved today? (Round your answer to 2 decimal places.) Number of Problems (a-2) What is the standard deviation? (Round your answer to 4 decimal places.) Standard Deviation (b) What is the probability 30 of the problems can be resolved today? (Round your answer to 4 decimal places.) Probability (c) What is the probability 30 or 31 of the problems can be resolved today? (Round your answer to 4 decimal places.) Probability (d) What is the probability more than 30 of the problems can be resolved today? (Round your answer to 4 decimal places.) Probability

Explanation / Answer

Ans:

Use Binomial distribution with n=35,p=0.75

P(x=r)=35Cr*0.75r*(1-0.75)35-r

a)Expectation=np=35*0.75=26.25

b)standard deviation=sqrt(35*0.75*(1-0.75))=2.5617

c)P(x=30)=35C30*0.7530*(1-0.75)5=0.0566

d)P(x=30 or 31)=P(x=30)+P(x=31)

=0.0566+35C31*0.7531*(1-0.75)4

=0.0566+0.0274

=0.0840

d)

P(x>30)=1-P(x<=30)=1-binomcdf(35,0.75,30)

=0.0410

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