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

Algebra ->  Probability-and-statistics -> 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       Log On


   

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) About Me  (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