Question

Edith Educationer has a real problem with children’s television programs. She believes there are too many commercials in them. To study this, she collects a sample of 500 children’s programs (n = 500) and counts how many commercials are on during the program. The frequency count of programs with the number of commercials is found below:

Commercials, X	8	9	10	11	12
Frequency	50	75	150	125	100
P(X)

Complete the table to produce the general discrete probability distribution. Use this probability distribution to answer questions a – h.

1. How many commercials, X, is the most likely outcome to occur?
2. Find the average number and standard deviation of commercials a child will expect to see in a program.

3. What is the probability that a child will see 10 or more commercials when watching a program? P(X ≥ 10)
4. What is the probability that a child will watch 4 commercials? P(X < 4)
5. What is the probability that a child will watch exactly 12 commercials? P(X = 12)
6. What is the probability that a child will watch exactly 7 commercials? P(X = 7)
7. What is the expected number of commercials in a program?
8. Graph the probability Distribution

Answer 1

X	8	9	10	11	12
Frequency	50	75	150	125	100
Probability	0.1	0.15	0.3	0.25	0.2

The above probabilities are computed by dividing the frequency by total number of students that is 500 in this case.

a) Most likely outcome is with highest probability that is 10 commercials

b) The average number of commercials is computed as:

Therefore

Therefore the mean is 10.3 commercials and standard deviation is 1.2288

c) P(X >= 10) = 0.3 + 0.25 + 0.2 = 0.75

d) P(X < 4) = 0

e) P(X = 12) = 0.2

f) P(X = 7) = 0