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 78% of the cases. Suppose the 14 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 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.)

Probability

  

d.	What is the probability more than 9 of the problems can be resolved today? (Round your answer to 4 decimal places.)

Probability

Answer 1

a)

Number of problems= n p

= 14 * 0.78
= 10.92

b)

std.dev = sqrt(npq)
= sqrt(14 * 0.78 *(1-0.78))
= 1.5500

c)

Here, n = 14, p = 0.78, (1 - p) = 0.22 and x = 8
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 8)
P(X = 8) = 14C8 * 0.78^8 * 0.22^6
P(X = 8) = 0.0466
0

d)
Here, n = 14, p = 0.78, (1 - p) = 0.22, x1 = 8 and x2 = 9.
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(8 <= X <= 9)
P(8 <= X <= 9) = (14C8 * 0.78^8 * 0.22^6) + (14C9 * 0.78^9 * 0.22^5)
P(8 <= X <= 9) = 0.0466 + 0.1103
P(8 <= X <= 9) = 0.1569

e)

Here, n = 14, p = 0.78, (1 - p) = 0.22, x1 = 9 and x2 = 9.
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X > 9).
P(X <= 9) = (14C0 * 0.78^0 * 0.22^14) + (14C1 * 0.78^1 * 0.22^13) + (14C2 * 0.78^2 * 0.22^12) + (14C3 * 0.78^3 * 0.22^11) + (14C4 * 0.78^4 * 0.22^10) + (14C5 * 0.78^5 * 0.22^9) + (14C6 * 0.78^6 * 0.22^8) + (14C7 * 0.78^7 * 0.22^7) + (14C8 * 0.78^8 * 0.22^6) + (14C9 * 0.78^9 * 0.22^5)
P(X <= 9) = 0 + 0 + 0 + 0 + 0.0001 + 0.0007 + 0.0037 + 0.015 + 0.0466 + 0.1103
P(X <= 9) = 0.1764

P(X > 9) = 1 - P(x< =9)
= 1 - 0.1764
= 0.8236