Question

In: Statistics and Probability

A commuter must pass through five traffic lights on her way to work and will have...

A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits (x), as shown below:

x 0 1 2 3 4 5
p(x) 0.03 0.21 p 0.1 0.1 0.05

Find the probability that she hits at most 3 red lights. Answer to 2 decimal places.

Tries 0/5

Find the probability that she hits at least 3 red lights. Answer to 2 decimal places.

Tries 0/5

How many red lights she expect to hit? Answer to 2 decimal places.

Tries 0/5

What is the standard deviation of number of red lights she hits? Answer to 3 decimal places.

Tries 0/5

Let us consider any two consecutive days. What is the chance that she hits exactly two red lights on both days? Answer to 4 decimal places.

Solutions

Expert Solution

The Table given

x 0 1 2 3 4 5
p(x) 0.03 0.21 p 0.1 0.1 0.05

We know for probability function  

Therefore ,

Probability that she hits at most 3 red lights

Probability that she hits at most 3 red lights is 0.85

Probability that she hits atleast 3 red lights

Probability that she hits atleast 3 red lights is 0.25

Number of red lights she expect to hit

Red lights she expect to hit is 2.18

Standard deviation

Standard deviation of number of red lights she hits is 1.117

Probability she hits excatly two red lights on both days

The chance that she hits excatly two red lights on both days is 0.2601


Related Solutions

A commuter must pass through five traffic lights on her way to work and will have...
A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits (x), as shown below: x 0 1 2 3 4 5 p(x) 0.04 0.23 p 0.1 0.1 0.1 a)Find the probability that she hits at most 3 red lights. Answer to 2 decimal places. b)Find the probability that she hits at least 3...
Another student must pass through 12 sets of traffic lights on his way to university each...
Another student must pass through 12 sets of traffic lights on his way to university each day. Suppose that each of the lights is green 36% of the time, yellow 5% of the time, and red 59% of the time. Suppose it is known that the traffic lights function independently. (a) What is the probability that the student encounters exactly five red lights on his way to university one day? (b) What is the probability that the student encounters at...
A daily commuter crosses two traffic signals on his way to work. The probability that he...
A daily commuter crosses two traffic signals on his way to work. The probability that he will be stopped at the first signal is 0.47, at the second signal is 0.30, and the probability that he may not have to stop at any of the two signals is 0.3. Answer all the questions to 2 decimal places where appropriate. 1. What is the probability that the commuter will be stopped at both signals? 2. What is the probability that he...
5. A driver encounters two traffic lights on the way to work each morning. Each light...
5. A driver encounters two traffic lights on the way to work each morning. Each light is either red, yellow, or green. The probabilities of the various combinations of colors is given in the following table: Second Light First Light R Y G R 0.31 0.02 0.18 Y 0.02 0.03 0.03 G 0.14 0.04 0.23 a) What is the probability that the first light is red? b) What is the probability that the second light is green? c) Find the...
There are two traffic lights on a commuter's route to and from work. Let X1 be...
There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). x1 0 1 2 μ...
There are two traffic lights on a commuter's route to and from work. Let X1 be...
There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning home from work. Suppose these two variables are independent, each with pmf given in the accompanying table. (so X1, X2 is a random sample size n=2.) x1 = 0 1 2 p(x1)= .2 .5 .3...
There are two traffic lights on a commuter's route to and from work. Let X1 be...
There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). x1 0 1 2 p(x1)...
There are two traffic lights on a commuter's route to and from work. Let X1 be...
There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). x1 0 1 2 μ...
There are two traffic lights on a commuter's route to and from work. Let X1 be...
There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). x1 0 1 2 μ...
A Bloomington resident commutes to work in Indiannapolis, and he encounters several traffic lights on the...
A Bloomington resident commutes to work in Indiannapolis, and he encounters several traffic lights on the way to work each day. Over a period of time, the following pattern has emerged: - Each day the first light is green - If a light is green, then the next one is always red - If he encounters a green light and then a red one, then the next will be green with probability 0.6 and red with probability .4. - If...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT