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Two cars A and B are travelling independently in the same direction. The speed of car A is normally distribution with the mean 100 kilometers per hour standard deviation5 kilometers per hour and the speed of car B is normally distributed with the mean 100
kilometers per hour a standard deviation 2 kilometer per hour. Initially (at time t = 0) the car A is 3 kilometers ahead of car B. Find the probability that after 3 hours these two cars will be
within of 3 kilometers?
kilometers per hour a standard deviation 2 kilometer per hour. Initially (at time t = 0) the car A is 3 kilometers ahead of car B. Find the probability that after 3 hours these two cars will be
within of 3 kilometers?
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Two cars A and B are travelling independently in the same direction. T...
Problem Overview
Two cars, A and B, are traveling in the same direction with different speeds. Car A is initially 3 kilometers ahead of car B. We need to determine the probability that after 3 hours, the two cars will be within 3 kilometers of each other.
Speed Distributions
- Car A:
- Speed follows a normal distribution:
- Mean = 100 km/h
- Standard deviation = 5 km/h
- Car B:
- Speed follows a normal distribution:
- Mean = 100 km/h
- Standard deviation = 2 km/h
Distance Calculation After 3 Hours
- Distance covered by Car A after 3 hours (X):
- X = Speed of A * 3 hours
- X ~ N(300, 45)
- (300 is the mean; 45 is the variance = 5^2 * 3)
- Distance covered by Car B after 3 hours (Y):
- Y = Speed of B * 3 hours
- Y ~ N(300, 12)
- (300 is the mean; 12 is the variance = 2^2 * 3)
Relative Position After 3 Hours
- New position of Car A = 3 + X
- New position of Car B = Y
- Difference in position (D):
- D = (3 + X) - Y
- D ~ N(3, 57)
- (3 is the mean; 57 is the variance = 45 + 12)
Probability Calculation
- We need to find P(-3 < d="" />< />
- Standardize: Z = (D - 3) / sqrt(57)
- Find P(-3 < z="" />< 3)="" using="" standard="" normal="" distribution="" />
Conclusion
- This will yield the desired probability that the two cars will be within 3 kilometers of each other after 3 hours.
Two cars, A and B, are traveling in the same direction with different speeds. Car A is initially 3 kilometers ahead of car B. We need to determine the probability that after 3 hours, the two cars will be within 3 kilometers of each other.
Speed Distributions
- Car A:
- Speed follows a normal distribution:
- Mean = 100 km/h
- Standard deviation = 5 km/h
- Car B:
- Speed follows a normal distribution:
- Mean = 100 km/h
- Standard deviation = 2 km/h
Distance Calculation After 3 Hours
- Distance covered by Car A after 3 hours (X):
- X = Speed of A * 3 hours
- X ~ N(300, 45)
- (300 is the mean; 45 is the variance = 5^2 * 3)
- Distance covered by Car B after 3 hours (Y):
- Y = Speed of B * 3 hours
- Y ~ N(300, 12)
- (300 is the mean; 12 is the variance = 2^2 * 3)
Relative Position After 3 Hours
- New position of Car A = 3 + X
- New position of Car B = Y
- Difference in position (D):
- D = (3 + X) - Y
- D ~ N(3, 57)
- (3 is the mean; 57 is the variance = 45 + 12)
Probability Calculation
- We need to find P(-3 < d="" />< />
- Standardize: Z = (D - 3) / sqrt(57)
- Find P(-3 < z="" />< 3)="" using="" standard="" normal="" distribution="" />
Conclusion
- This will yield the desired probability that the two cars will be within 3 kilometers of each other after 3 hours.
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Two cars A and B are travelling independently in the same direction. The speed of car A is normally distribution with the mean 100 kilometers per hour standard deviation5 kilometers per hour and the speed of car B is normally distributed with the mean 100kilometers per hour a standard deviation 2 kilometer per hour. Initially (at time t = 0) the car A is 3 kilometers ahead of car B. Find the probability that after 3 hours these two cars will bewithin of 3 kilometers?
Question Description
Two cars A and B are travelling independently in the same direction. The speed of car A is normally distribution with the mean 100 kilometers per hour standard deviation5 kilometers per hour and the speed of car B is normally distributed with the mean 100kilometers per hour a standard deviation 2 kilometer per hour. Initially (at time t = 0) the car A is 3 kilometers ahead of car B. Find the probability that after 3 hours these two cars will bewithin of 3 kilometers? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Two cars A and B are travelling independently in the same direction. The speed of car A is normally distribution with the mean 100 kilometers per hour standard deviation5 kilometers per hour and the speed of car B is normally distributed with the mean 100kilometers per hour a standard deviation 2 kilometer per hour. Initially (at time t = 0) the car A is 3 kilometers ahead of car B. Find the probability that after 3 hours these two cars will bewithin of 3 kilometers? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cars A and B are travelling independently in the same direction. The speed of car A is normally distribution with the mean 100 kilometers per hour standard deviation5 kilometers per hour and the speed of car B is normally distributed with the mean 100kilometers per hour a standard deviation 2 kilometer per hour. Initially (at time t = 0) the car A is 3 kilometers ahead of car B. Find the probability that after 3 hours these two cars will bewithin of 3 kilometers?.
Two cars A and B are travelling independently in the same direction. The speed of car A is normally distribution with the mean 100 kilometers per hour standard deviation5 kilometers per hour and the speed of car B is normally distributed with the mean 100kilometers per hour a standard deviation 2 kilometer per hour. Initially (at time t = 0) the car A is 3 kilometers ahead of car B. Find the probability that after 3 hours these two cars will bewithin of 3 kilometers? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Two cars A and B are travelling independently in the same direction. The speed of car A is normally distribution with the mean 100 kilometers per hour standard deviation5 kilometers per hour and the speed of car B is normally distributed with the mean 100kilometers per hour a standard deviation 2 kilometer per hour. Initially (at time t = 0) the car A is 3 kilometers ahead of car B. Find the probability that after 3 hours these two cars will bewithin of 3 kilometers? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cars A and B are travelling independently in the same direction. The speed of car A is normally distribution with the mean 100 kilometers per hour standard deviation5 kilometers per hour and the speed of car B is normally distributed with the mean 100kilometers per hour a standard deviation 2 kilometer per hour. Initially (at time t = 0) the car A is 3 kilometers ahead of car B. Find the probability that after 3 hours these two cars will bewithin of 3 kilometers?.
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Two cars A and B are travelling independently in the same direction. The speed of car A is normally distribution with the mean 100 kilometers per hour standard deviation5 kilometers per hour and the speed of car B is normally distributed with the mean 100kilometers per hour a standard deviation 2 kilometer per hour. Initially (at time t = 0) the car A is 3 kilometers ahead of car B. Find the probability that after 3 hours these two cars will bewithin of 3 kilometers?, a detailed solution for Two cars A and B are travelling independently in the same direction. The speed of car A is normally distribution with the mean 100 kilometers per hour standard deviation5 kilometers per hour and the speed of car B is normally distributed with the mean 100kilometers per hour a standard deviation 2 kilometer per hour. Initially (at time t = 0) the car A is 3 kilometers ahead of car B. Find the probability that after 3 hours these two cars will bewithin of 3 kilometers? has been provided alongside types of Two cars A and B are travelling independently in the same direction. The speed of car A is normally distribution with the mean 100 kilometers per hour standard deviation5 kilometers per hour and the speed of car B is normally distributed with the mean 100kilometers per hour a standard deviation 2 kilometer per hour. Initially (at time t = 0) the car A is 3 kilometers ahead of car B. Find the probability that after 3 hours these two cars will bewithin of 3 kilometers? theory, EduRev gives you an
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