Answer:
Mean = 22
Variance = 13.1320
Standard Deviation = 3.6238
Step-by-step explanation:
From the question, we can deduce that
n = 55 (sample)
p = 39.4% (proportion of those within the given range)
Solving (a): Expected Value, E(x)
This is calculated using the following formula.
E(x) = np
Substitute values for n and p
E(x) = 55 * 39.4%
E(x) = 55 * 0.394
E(x) = 21.67
E(x) = 22 ---- Approximated
Hence, the expected number of people is 22
Solving (b): Variance (σ²) and Standard Deviation (σ)
σ² is calculated as thus:
σ² = np(1 - p)
σ² = 55 * 39.4% * (1 - 39.4%)
σ² = 55 * 0.394 * (1 - 0.394)
σ² = 55 * 0.394 * 0.606
σ² = 13.13202
σ² = 13.1320 ---- Approximated
σ is calculated as follows:
σ = √σ²
Substitute value for σ²
σ = √13.13
σ = 3.6238 ----- Approximated
