An
μ Y=103 dollars
σ Y≈64.8 dollars
Step-by-step explanation:
We can find her income by multiplying the number of customers by 606060, and then subtracting her fixed transportation cost to get her net gain:
Y=60X-5Y=60X−5Y, equals, 60, X, minus, 5
How will this transformation impact the mean and standard deviation?
Hint #22 / 4
Effect on mean
Multiplying by 606060 and subtracting 555 both impact the mean:
\begin{aligned} \mu_Y&=60\left(\mu_X\right)-5 \\\\ &=60\left(1.8\right)-5 \\\\ &=108-5 \\\\ &=103 \end{aligned}
μ
Y
=60(μ
X
)−5
=60(1.8)−5
=108−5
=103
Hint #33 / 4
Effect on standard deviation
Multiplying by 606060 impacts the standard deviation, but subtracting 555 does not — adding or subtracting a constant only shifts data, which doesn't affect the spread.
\begin{aligned} \sigma_Y&=60\left(\sigma_X\right) \\\\ &\approx60\left(1.08\right) \\\\ &\approx64.8 \end{aligned}
σ
Y
=60(σ
X
)
≈60(1.08)
≈64.8
