Question

1. the bank of america vp feels that each savings account customer has, on average, three credit cards. the following distribution represents the number of credit cards people own.

x 0 1 2 3 4
p(x) 0.18 0.44 0.27 0.08 0.03

a. find the mean, variance, and standard deviation.

e(x) μ=
σ²=
σ=

b. is the vp correct?

Explanation:

Step1: Calculate the mean

The formula for the mean \(\mu = E(X)=\sum_{i}x_{i}P(x_{i})\)

$$
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$$

Step2: Calculate the variance

The formula for the variance \(\sigma^{2}=\sum_{i}(x_{i}-\mu)^{2}P(x_{i})\)

$$
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$$

Step3: Calculate the standard deviation

The formula for the standard deviation \(\sigma=\sqrt{\sigma^{2}}\)

$$ \sigma=\sqrt{0.9244}\approx0.9615 $$

Step4: Answer part b

Since the mean number of credit cards \(\mu = 1.34
eq3\), the VP is not correct.

Answer:

a. Mean \(\mu = 1.34\), Variance \(\sigma^{2}=0.9244\), Standard deviation \(\sigma\approx0.9615\)
b. The VP is not correct.