Question

The speed with which utility companies can resolve problems is very important. The Georgetown Telephone Company (GTC), reports that it can resolve customer problems the same day they are reported in 67% of the cases. Suppose that the 23 cases reported today are representative of all complaints. a-1. How many of the problems would you expect to be resolved today? (Round the final answer to 2 decimal places.) Number of Problems a-2. What is the standard deviation? (Round the final answer to 4 decimal places.) Standard Deviation b. What is the probability that 18 of the problems can be resolved today? (Round the final answer to 4 decimal places.) Probability c. What is the probability that 18 or 19 of the problems can be resolved today? (Round the final answer to 4 decimal places.) Probability d. What is the probability that more than 18 of the problems can be resolved today? (Round the final answer to 4 decimal places.) Probability

statsistics

Answer 1

here this is binomial with parameter n=23 and p=0.67

a-1_)

mean E(x)=μ=np=15.41

a-2)

standard deviation σ=√(np(1-p))=2.2551

b()

P(X=18)=

(nCx)px(1−p)(n-x)    =

0.0975

if using ti-84 use commannd :binompdf(23,0.67,18)

if using excel use commannd :binomdist(18,23,0.67,false)

c)

P(18<=X<=19)=

∑x=ab     (nCx)px(1−p)(n-x)    =

0.1496

if using ti-84 use commannd :binomcdf(23,0.67,19)-binomcdf(23,0.67,17)

if using excel use commannd :binomdist(19,23,0.67,true)-binomdist(17,23,0.67,true)

d)

P(X>=19)=1-P(X<=18)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.0806

if using ti-84 use commannd :1-binomcdf(23,0.67,18)

if using excel use commannd :1-binomdist(18,23,0.67,true)