Speeding on the I-5. The distribution of speeds of cars traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 72.6 miles/hour and a standard deviation of 4.78 miles/hour. The speed limit on this stretch of the I-5 is 70 miles/hour. (a) A highway patrol officer is hidden on the side of the freeway. What is the probability that 5 cars pass and none are speeding? Assume that the speeds of the cars are independent of each other. (b) On average, how many cars would the highway patrol officer expect to watch until the first car that is speeding? What is the standard deviation of the number of cars he would expect to watch?
Added by Taylor R.
Step 1
(a) Show more…
Show all steps
Close
Your feedback will help us improve your experience
Ameer Said and 95 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The distribution of passenger vehicle speeds traveling on a certain freeway in California is nearly normal with a mean of 72.8 miles/hour and a standard deviation of 4.76 miles/hour. The speed limit on this stretch of the freeway is 70 miles/hour. (a) A highway patrol officer is hidden on the side of the freeway. What is the probability that 5 cars pass and none are speeding? Assume that the speeds of the cars are independent of each other. (Round your answer to four decimal places.) (b) On average, how many cars would the highway patrol officer expect to watch until the first car that is speeding? (Round your answer to two decimal places.) What is the standard deviation of the number of cars he would expect to watch? (Round your answer to two decimal places.)
Nicholas H.
The distribution of passenger vehicle speeds traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 72.6 miles/hour and a standard deviation of 4.78 miles/hour. (a) What percent of passenger vehicles travel slower than 80 miles/hour? (b) What percent of passenger vehicles travel between 60 and 80 miles/hour? (c) How fast do the fastest 5% of passenger vehicles travel? (d) The speed limit on this stretch of the I-5 is 70 miles/hour. Approximate what percentage of the passenger vehicles travel above the speed limit on this stretch of the I-5. (e) A highway patrol officer is hidden on the side of the freeway. What is the probability that 5 cars pass and none are speeding? Assume that the speeds of the cars are independent of each other.
Gaurav K.
Vehicle speed on a particular bridge in China can be modeled as normally distributed ("Fatigue Reliability Assessment for Long-Span Bridges under Combined Dynamic Loads from Winds and Vehicles," J. of Bridge Engr., $2013 : 735-747 )$ . (a) If 5$\%$ of all vehicles travel less than 39.12 $\mathrm{mph}$ and 10$\%$ travel more than 73.24 $\mathrm{mph}$ , what are the mean and standard deviation of vehicle speed? [Note: The resulting values should agree with those given in the cited article.] (b) What is the probability that a randomly selected vehicle's speed is between 50 and 65 $\mathrm{mph}$ ? (c) What is the probability that a randomly selected vehicle's speed exceeds the speed limit of 70 $\mathrm{mph} ?$
Continuous Random Variables and Probability Distributions
The Normal (Gaussian) Distribution
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD