Answer:
The mean of C is 170 households
The standard deviation of C, is approximately 5 households
Step-by-step explanation:
The given parameters are;
The percentage of households in the United States that had a computer in 2014 = 85%
The size of the randomly selected sample in 2014, n = 200
The random variable representing the number of households that had a computer = C
Therefore, we have;
The probability of a household having a computer P = 85/100 = 0.85
Let
Therefore;
The mean (expected) number in the sample, μₓ, = E(x) = n × P is given as follows;
μₓ = 200 × 0.85 = 170
The mean of C = μₓ = 170
The variance, σ² = n × P × (1 - P) = 200 × 0.85 × (1 - 0.85) = 25.5
Therefore;
The standard deviation, σ = √(σ²) = √(25.5) ≈ 5.05
The standard deviation of C, σ ≈ 5 households (we round (down) to the nearest whole number)
