A local television station sells 15-sec, 30-sec, 45-sec, and 60-sec advertising

Question

A local television station sells 15-sec, 30-sec, 45-sec, and 60-sec advertising spots.Let x denote the length of a randomly selected advertisement time on this station, and suppose that the corresponding number of commercials per week is given below:

x

Number of Commercials

f(x)

15

50

30

125

45

140

60

185

      A) Use the data to develop an empirical discrete probability distribution for x.

      B) Show that your probability distribution satisfies the conditions for a valid discrete probability distribution.

      C) Compute E(x), the average length for advertisement time on this station.

      D) Compute Var(x), the variance of x, and , the standard deviation of x

      E) What is the probability that the number of commercials is less than 45 seconds?

x

Number of Commercials

f(x)

15

50

30

125

45

140

60

185

Explanation / Answer

P( number of commercials is less than 45 seconds) = 0.25 +0.1 = 0.35

x Number of commercials P(X) x*P(x) x^2*P(x) 15 50 0.1 1.5 22.5 30 125 0.25 7.5 225 45 140 0.28 12.6 567 60 185 0.37 22.2 1332 total 500 1 43.8 2146.5 E(X) 43.8 V(X) 2146.5 - 43.8^2 V(X) 228.06

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.