Question

The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes.1. What is the probability that you have to wait more than 30 seconds for the light?A) 0.25
B) 0.50
C) 0.75
D) 1.012. What is the probability that you have to wait between 15 and 45 seconds for the light?A) 0.15
B) 0.25
C) 0.35
D) 0.453. Eighty percent of the time, the light will change before you have to wait how long?A) 90 seconds
B) 24 seconds
C) 30 seconds
D) 96 seconds

Answer 1

Answer:

1. Option C) 0.75

2. Option B) 0.25

3. Option D) 96 seconds

Step-by-step explanation:

1. The waiting time is between 0 and 2 minutes. We can say that the time can be distributed according to the following expression:

0 ≤ x ≤ 0

where x is the time between 0 and 2 minutes.

A time more than 30 seconds leaves the remaining time:

2 mins  = 120 sec

30 seconds off = 120 - 30

                         = 90

Therefore, the probability is = $\frac{90}{120} \\ = \frac{3}{4}\\ = 0.75$

2. between 15 and 45 seconds

the time will be = 45 - 15

                          = 30 seconds

therefore, the probability will be $\frac{30}{120}\\ = \frac{1}{4}\\ = 0.25$

3. 80 %  the light will change after the following time = 80% × 120 s

                                                                                         = 0.8 × 120

                                                                                         = 96 seconds