Question

he 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

statistics

Answer 1

X ~ Bin ( n , p)

n = 23 , p = 0.67

a)

E(X) = n * p = 23 * 0.67

= ²³15.41

Standard deviation = sqrt [ n p ( 1 - p) ]

= sqrt [ 23 * 0.67 ( 1 - 0.67) ]

= 2.2551

b)

Binomial probability distribution is

P(X) = nCx p^x ( 1 - p)^n-x

P(X = 18) = ²³C₁₈ * 0.67¹⁸ * ( 1 - 0.67)⁵

= 0.0975

c)

P(X = 18 OR 19) = P(X = 18) + P(X = 19)

= ²³C₁₈ * 0.67¹⁸ * ( 1 - 0.67)⁵ +²³C₁₉ * 0.67¹⁹ * ( 1 - 0.67)⁴

= 0.1496

d)

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

= 1 - BINOM.DIST(18, 23 , 0.67, TRUE)

= 1 - 0.9194

= 0.0806