Answer
Mean = μ = ∑X * P(X)
= (0*0.18)+(1*0.44)+(2*0.27)+(3*0.08)+(4*0.03)
= 1.34
Variance = $ σ ^{2}$ = ∑[$X ^{2}$ * P(X)] - $ μ ^{2}$
=[ $0 ^{2}$ *0.18 +$ 1 ^{2}$ * 0.44 + $ 2 ^{2}$ * 0.27 + $ 3 ^{2}$ *0.08 + $ 4 ^{2}$ *0.03 ] -$ 1.34 ^{2}$
=(0+0.44+1.08+0.72+0.48)-1.7956
=2.72-1.7956
=0.9244
Standard Deviation = σ = $ \sqrt σ ^{2}$ = $\sqrt 0.9244$ = 0.9615
The vice president is incorrect since the mean number of credit card own is 1.34 with a deviation of 0.9615. Based on Chebyshev's Theorem, μ + 2σ = 3.263 ~ 4 with a confidence of 75% is owning 4 credit card instead of 3.
Work Step by Step
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