Question

The National Household Travel Survey gathers data on the time of day when people begin a trip in their car or other vehicle.

Choose a trip at random and record the time at which the trip started. Here is an assignment of probabilities for the outcomes:
5 Time of day
Probability
Time of
Day
Probability
Time of day
Probability
10 p.m. 12:59 1 a.m. -5:59 6 a.m. - 8:59
a.m.
0.144
4p.m. - 6:59
p.m.
?
a.m.
0.040
9 a.m. - 12:59 1 p.m. -3:59
p.m.
0.234
7 p.m. - 9:59
a.m.
0.033
p.m.
0.123
p.m.
0.208
What probability should replace "?" in the table?
0.782
0.442
0.218
0.558
0.143

Answer 1

To find the missing probability for the 4 p.m. - 6:59 p.m. time slot, we calculate it by subtracting the sum of known probabilities from 1. The calculation results in a missing probability of 0.218.

Step-by-step explanation:

The question asks to find the missing probability for the time slot of 4 p.m. - 6:59 p.m. in a given probability distribution table. The sum of all probabilities in a complete distribution must equal 1. Given the probabilities for other time slots, we can calculate the missing probability by subtracting the sum of the known probabilities from 1.

The known probabilities are:

• 10 p.m. - 12:59 a.m.: 0.144
• 1 a.m. - 5:59 a.m.: 0.040
• 6 a.m. - 8:59 a.m.: 0.033
• 9 a.m. - 12:59 p.m.: 0.234
• 1 p.m. - 3:59 p.m.: 0.123
• 7 p.m. - 9:59 p.m.: 0.208

Adding these probabilities gives us a total of:

0.144 + 0.040 + 0.033 + 0.234 + 0.123 + 0.208 = 0.782

The probability that replaces is:

1 - 0.782 = 0.218