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 68% of the cases. Suppose that the 16 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 11 of the problems can be resolved today? (Round the final answer to 4 decimal places.)

Probability          

c. What is the probability that 11 or 12 of the problems can be resolved today? (Round the final answer to 4 decimal places.)

Probability          

d. What is the probability that more than 11 of the problems can be resolved today? (Round the final answer to 4 decimal places.)

Probability          

Answer 1

p = 0.68

n = 16

A-1) expected value = n * p = 16 * 0.68 = 10.88

A-2) standard deviation = sqrt(n * p * (1-p)) = sqrt(16 * 0.68 * 0.32) = 1.8659

B) P(X = 11) = 16C11 * 0.68¹¹ * 0.32⁵ = 0.2107

C) P(X = 11 or 12) = P(X = 11) + P(X = 12)

= 0.2107 + 16C12 * 0.68¹² * 0.32⁴

= 0.2107 + 0.1865

= 0.3972

D) P(X > 11) = P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)

= 16C12 * 0.68¹² * 0.32⁴ + 16C13 * 0.68¹³ * 0.32³ + 16C14 * 0.68¹⁴ * 0.32² + 16C15 * 0.68¹⁵ * 0.32¹ + 16C16 * 0.68¹⁶ * 0.32⁰

= 0.3819