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

a) X    1       2      3       4       5

P(X) 0.7  0.15  0.10  0.03  0.02

b)

c)

d)

e)

Step-by-step explanation:

Part a

From the information given we define the probability distribution like this:

X       1       2      3       4       5

P(X) 0.7  0.15  0.10  0.03  0.02

And we see that the sum of the probabilities is 1 so then we have a probability distribution

Part b

We want to find this probability:

Part c

We want to find this probability

And for this case we can use the complement rule and we got:

Part d

We can find the expected value with this formula:

Part e

For this case we need to find first the second moment given by:

And we can find the variance with the following formula:

And we can find the deviation taking the square root of the variance:

$9.41

step-by-step explanation: