the following table gives the number of camcorders sold on a given day in an electronics store
X: 0, 1, 2, 3, 4, 5, 5,
P(x) 0.5, .12, .23, .3, .16, .1, .04
find the mean, variance, and standard deviation of the daily sales of camcorders in the store.
Mean = 0(.5) + 1(.12) + 2( .23) + 3(.3) + 46.16) + 5(.1) +5 (.04) = ?
variance = 0^2(.5) + 1^2(.12) + 2^2 (.23) + 3^2(.3) + 4^2(.16) +5^2 (.1) + 5^2(.04) = ?
Standard deviation = sqrt(variance -mean ^2))
3,96
To find the mean, variance, and standard deviation of the daily sales of camcorders in the store, we'll use the given table of the number of camcorders sold (X) and the corresponding probabilities (P(x)).
Step 1: Calculate the mean (μ):
The mean is calculated by multiplying each value of X by its corresponding probability and then summing the products.
μ = ∑(X * P(x))
μ = (0 * 0.5) + (1 * 0.12) + (2 * 0.23) + (3 * 0.3) + (4 * 0.16) + (5 * 0.1) + (5 * 0.04)
μ = 0 + 0.12 + 0.46 + 0.9 + 0.64 + 0.5 + 0.2
μ = 2.82
So, the mean daily sales of camcorders in the store is 2.82.
Step 2: Calculate the variance (σ²):
The variance is calculated by summing the squared difference between each value of X and the mean, multiplied by its corresponding probability.
σ² = ∑((X - μ)² * P(x))
σ² = ((0 - 2.82)² * 0.5) + ((1 - 2.82)² * 0.12) + ((2 - 2.82)² * 0.23) + ((3 - 2.82)² * 0.3) + ((4 - 2.82)² * 0.16) + ((5 - 2.82)² * 0.1) + ((5 - 2.82)² * 0.04)
σ² = (7.9524 * 0.5) + (2.2848 * 0.12) + (0.2392 * 0.23) + (0.018 * 0.3) + (0.1376 * 0.16) + (4.8684 * 0.1) + (4.8684 * 0.04)
σ² = 3.9762 + 0.2742 + 0.0551 + 0.0054 + 0.022 + 0.4868 + 0.1947
σ² = 4.0144
So, the variance of the daily sales of camcorders in the store is 4.0144.
Step 3: Calculate the standard deviation (σ):
The standard deviation is the square root of the variance.
σ = √(σ²)
σ = √(4.0144)
σ ≈ 2.003
So, the standard deviation of the daily sales of camcorders in the store is approximately 2.003.