The speed with which utility companies can resolve problems is very important. G
ID: 3368455 • Letter: T
Question
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 76% of the cases. Suppose the 14 cases reported today are representative of all c a-1. How many of the problems would you expect to be resolved today? (Round your answer to 2 decimal places.) ber of Problems a-2. What is the standard deviation? (Round your answer to 4 decimal places.) b. What is the probability 8 of the problems can be resolved today? (Round your answer to 4 decimal places.) Probability c. What is the probability 8 or 9 of the problems can be resolved today? (Round your answer to 4 decimal places.) Probabilit d. What is the probability more than 9 of the problems can be resolved today? (Round your answer to 4 decimal places.) ProbabilityExplanation / Answer
we are given
p=76% =0.76
n=14
q=1-p =1-0.76 =0.24
a1)
number of problems = Expected number,E =n*p
= 14 * 0.76
=10.64
a2)
standard deviation = sqrt(npq)
=sqrt(14*0.76*0.24)
=sqrt(2.5536)
=1.5980
b)
P(x=8) =nCr p^r q^(n-r)
= 14C8 (0.76)^8 (0.24)^(14-8)
=3003 * (0.76)^8 (0.24)^6
=0.0639
c)
P(x=8 or 9) =P(x=8) + P(x=9)
=14C8 (0.76)^8 (0.24)^(14-8) + 14C9 (0.76)^9 (0.24)^(14-9)
=3003 * (0.76)^8 (0.24)^6 + 2002 * (0.76)^9 (0.24)^5
=0.1987
d) P(more than 9) =P(x>9)
=1 - P(x<= 9)
= 1 - 0.229724
=0.7703
Please note that we calculate P(x<=9 ) using excel command as =BINOM.DIST(9,14,0.76,TRUE)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.