Question

# The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone...

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 75% of the cases. Suppose the 13 cases reported today are representative of all complaints.

How many of the problems would you expect to be resolved today? (Round your answer to 2 decimal places.)

What is the standard deviation? (Round your answer to 4 decimal places.)

What is the probability 10 of the problems can be resolved today? (Round your answer to 4 decimal places.)

What is the probability 10 or 11 of the problems can be resolved today? (Round your answer to 4 decimal places.)

What is the probability more than 8 of the problems can be resolved today? (Round your answer to 4 decimal places.)

Problem on binomial distribution with n-13 and p=0.75

How many of the problems would you expect to be resolved today? (Round your answer to 2 decimal places.)

expected mean=np=13*0.75=9.75

What is the standard deviation? (Round your answer to 4 decimal places.

standard devaition=sqrt(npq)

q=1-p

so standard deviation=sqrt(13*0.75*(1-0.75))=1.561249=1.5612

1.5612

What is the probability 10 of the problems can be resolved today? (Round your answer to 4 decimal places.)

P(X=10)

we have

P(X=x)=ncx*p^x*q^n-x

=13c10*0.75^10*0.25^13-10

=0.2517

0.2517

What is the probability 10 or 11 of the problems can be resolved today? (Round your answer to 4 decimal places.)

P(X=10)+P(X=11)

=13c10*0.75^10*0.25^13-10+13c11*0.75^11*0.25^13-11

=0.2517+0.2059

=0.4576

0.4576

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