Let X represent the number of occupants in a randomly chosen car on a certain stretch of highway during morning commute hours. A survey of cars showed that the probability distribution of X is as follows. x 1 2 3 4 5 P(x) 0.70 0.15 0.10 0.02 (a) Find P(4). (b) Find the probability that a car has at least 3 occupants. (c) Find the probability that a car has fewer than 3 occupants. (d) Compute the mean µX. (e) Compute the standard deviation σX.

a) P(4)=0.03

b) P(x≥3)=0.15

c) P(x<3)=0.85

d) µX=1.52

e) σX=1.69

Step-by-step explanation:

The question is incomplete:

The variable X has the following probability distribution:

x  1  2  3  4   5

P(x)0.70.150.100.03  0.02

a) The probability P(x=4) can be read from the table

b) The probability that there are at least 3 occupants in the car is P(x≥3).

c) The probability that a car has fewer than 3 occupants (P(x<3)) is:

d) The mean can be calculated as:

e) The standard deviation can be calculated as: