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 Xrepresent 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 μX.

e. Find σX

Step 1of 3 :

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.if X represent the number of occupants in a randomly chosen car.

We have to find

The probability mass function of X.P(X)P(X>3)E(X).Step 2 of 3:

It is given that 70% of the cars had only one occupant. 15% had 2, 10% had 3, 3% had 4, and 2% had 5. We can make a probability table based on this given data.so the probability mass function of X will be in the form.

(b) P( = P(X=1) +P(X=2)

= 0.70 +0.15

= 0.85.

Therefore the probability P= 0.85

(c) P(= 1- P(

= 1- [ P(X=1) +P( X=2 )+P(X =3) ]

= 1 - [0.70 + 0.15 +0.10 ]

= 1- 0.95

= 0.05.

So the probability that P(X>3) = 0.05 .