SOLUTION: Probability distributions Solve the following: 1. The Movies and Television Regulatory and Classification Board (MTRCB) determined the number of commercials shown in each of

Question 1190697: Probability distributions
Solve the following:
1. The Movies and Television Regulatory and Classification Board (MTRCB) determined
the number of commercials shown in each of the four night programs over a period of time. Find the mean, variance and standard deviation for the distribution below.
No. of Commercials (x) 10 11 12 13
Probability P(x) 0.15 0.35 0.30 0.20
2. The RFS Electronics sells iphones for Apple Inc. RFS usually sells the number of iphones on Sunday. The store manager established the following probability distribution for the number of Iphones the store expects to sell on a particular Sunday.
No. of Iphones (x) 0 1 2 3 4 5
Probability P(x) 0.05 0.10 0.12 0.15 0.18 0.40
How many Iphones should the store manager expect to sell? What is the variance and standard deviation of the distribution
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
**1. MTRCB Commercials**
* **Mean:** The mean (or expected value) is calculated by multiplying each value of x by its probability and summing the results:
Mean = (10 * 0.15) + (11 * 0.35) + (12 * 0.30) + (13 * 0.20) = 11.55
* **Variance:** The variance measures the spread of the distribution. It's calculated as the average of the squared differences from the mean:
Variance = [(10-11.55)² * 0.15] + [(11-11.55)² * 0.35] + [(12-11.55)² * 0.30] + [(13-11.55)² * 0.20] ≈ 0.9475
* **Standard Deviation:** The standard deviation is the square root of the variance:
Standard Deviation = √0.9475 ≈ 0.973
**2. RFS Electronics Iphones**
* **Expected Number of Iphones (Mean):** This is calculated the same way as the mean in the previous problem:
Expected Number = (0 * 0.05) + (1 * 0.10) + (2 * 0.12) + (3 * 0.15) + (4 * 0.18) + (5 * 0.40) = 3.51
* **Variance:** Calculate the variance using the same method as above:
Variance = [(0-3.51)² * 0.05] + [(1-3.51)² * 0.10] + [(2-3.51)² * 0.12] + [(3-3.51)² * 0.15] + [(4-3.51)² * 0.18] + [(5-3.51)² * 0.40] ≈ 2.4899
* **Standard Deviation:**
Standard Deviation = √2.4899 ≈ 1.578

RELATED QUESTIONS
Smart TVs have seen success in the United States market. During the 2nd quarter of 2015... (answered by ikleyn)

Whats the sum of t TVs and 11... (answered by stanbon)

The lifetime of a color television is normally distributed with a mean of 7.8 years and a (answered by Fombitz)

Manuela has a total of 40 dvds of movies and tv shows. The number of movies is 4 less... (answered by JulietG)

The lifetime of a color television is normally distributed with a mean of 7.8 years and a (answered by Fombitz)

The quality assurance engineer of a television manufacturer inspects TVs in lots of 100. (answered by ikleyn)

A company had 20 inch and 30 inch televisions is the ratio 4:7. 100 20 inch TVs were... (answered by Theo)

At a circuit city store 1/4 of those purchasing color televisions purchase a large screen (answered by Boreal)

In a shipment of 50 televisions, 5 are defective. If 2 television sets are randomly... (answered by brucewill)