The probability density function of a random variable X is f(x) = \(\frac{\pi}{10} sin \frac{\pi x}{5}\) ; 0 ≤ x ≤ 5. The first quartile of X is:
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Let G = college graduate, S = in sales. Given \(P(G)=0.60,\ P(G^{c})=0.40,\ P(S\mid G)=0.10,\ P(S\mid G^{c})=0.80\).
By the law of total probability:
\[P(S)=P(S\mid G)P(G)+P(S\mid G^{c})P(G^{c})\]
\[P(S)=(0.10)(0.60)+(0.80)(0.40)=0.06+0.32=0.38\]
Therefore the probability that a randomly selected employee is in sales is 0.38.
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