A survey of cars on a certain stretch of highway during morning commute hours showed that 70% had only one occupant, 15% had 2, 10% had 3, 3% had 4, and 2% had 5. Let X represent the number of occupants in a randomly chosen car.
a. Find the probability mass function of X.
b. Find P(X ? 2).
c. Find P(X > 3).
d. Find 
.
e. Find 
.
(a) 
(b) P(X ? 2) = P(X = 1) + P(X = 2) = 0.70 + 0.15 = 0.85
(c) P(X >3) = P(X = 4) + P(X = 5) = 0.03 + 0.02 = 0.05
(d) 
= 1(0.70) + 2(0.15) + 3(0.10) + 4(0.03) + 5(0.02) = 1.52
(e) 
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