Spectrum provides cable television and Internet service to over million customers. Suppose that the management of Spectrum subjectively assesses a probability distribution for the number of new subscribers next year in the state of New York as follows. 100,000 0.08 200,000 0.20 300,000 0.24 400,000 0.29 500,000 0.11 600,000 0.08 a. Is this probability distribution valid? Yes b. What is the probability Spectrum will obtain more than new subscribers? (to 2 decimals) c. What is the probability Spectrum will obtain fewer than new subscribers? (to 2 decimals)

a. Is this probability distribution valid? Yes b. What is the probability Spectrum will obtain more than 400,000 new subscribers? (to 2 decimals) c. What is the probability Spectrum will obtain fewer than 200,000 new subscribers? (to 2 decimals)

Answer:

Yes ; 0.19 ; 0.08

Step-by-step explanation:

Given the data:

__X_______p(X)

100,000___ 0.08

200,000__ 0.20

300,000__ 0.24

400,000__ 0.29

500,000___ 0.11

600,000___0.08

a. Is this probability distribution valid?

To determine validity of the distribution :

ΣP(X) must be equal to 1

(0.08 + 0.20 + 0.24 + 0.29 + 0.11 + 0.08) = 1

Hence, the distribution is valid.

What is the probability Spectrum will obtain more than 400,000 new subscribers

Probability of obtaining more than 400,000 new subscribers :

P > 400,000 = P(500,000) + P(600,000)

= 0.11 + 0.08 = 0.19

C.) What is the probability Spectrum will obtain fewer than 200,000 new subscribers?

P < 200,000 = P(100,000)

= 0.08